UPDATE: David Tait, of Skytrax Web Support, responded to a request for comment: "We are quite happy with the ASA response and statements, when they are read and used correctly!
A Skytrax statement says that since the ASA ruling the company has subsequently been:

'permitted to maintain full use of the established, key terminology such as 'official Skytrax 5-Star Airline" and related Official Skytrax Star Rating levels for all Airline and Airport Star Ranking Programmes.'
Meanwhile, in the UK market, the company has amended what it stated about ranking review frequency.
Full statement, including response to individual complaints, here.
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The UK regulator Advertising Standards Authority has upheld a complaint filed by KwikChex accusing airline review company Skytrax of misleading claims of authentic reviews.
London-based Skytrax, which bills itself as the "world's largest review site," was accused by KwikChex founder Chris Emmins of the following misleading claims:

1. the claims "Checked and trusted airline reviews" and "REAL travellers with REAL opinions!" were misleading and could not be substantiated, because they understood that Skytrax did not verify the reviews on their website and therefore could not prove that they were genuine;
2. the claim "More than 5 million independent, traveller reviews and customer trip ratings" was misleading and could not be substantiated;
3. the claim "Official Quality Star Ranking(TM)" was misleading, because it suggested that the ranking system was official and not the advertiser's own creation;
4. the claim "The Star Ranking programme operates in a real-time analysis format, to ensure that Airline Star Ranking levels are constantly maintained and adjusted in accordance with changes made by an airline, be this to product or service standards - on average, each airline's Star Ranking is reviewed in depth every 2-3 months, and adjusted in accordance with the annual ratings" was misleading and could not be substantiated, because they understood that the website continued to display rankings for airlines which were no longer in business; and
5. the claim "TRADEMARK(TM) PROTECTION - The titles below are protected by Skytrax, and can only be used by a Registered 5-Star Airline with consent of Skytrax" and accompanying list were misleading, because they did not believe that those titles were trademarked.
Each of these claims was upheld by the ASA, meaning that Skytrax was found in violation of ASA standards against "misleading, harmful or offensive advertising."
Skytrax responded to the complaint by outlining their verification procedures for each review.
The company asks for full name, country and email address, and sends a verification email within 24 hours to said email. Each verification email must be accessed within 24 hours for the review to be posted on site. All user verification details (including emails) are deleted after 24 hours, ostensibly to protect user privacy.
The company also claims to check each review for anything suspicious, inconsistent or strange that might mark it as a fake review.
The ASA determined that this was not sufficient to flag fake reviews, as the company could not provide follow-ups or proof that verification emails were actually sent for reviews currently posted on the site.
The ASA also found that Skytrax was misleading in advertising "millions" of user reviews, as their practice was to archive any reviews beyond the 10th page. This limits site users to a maximum available 400,000 reviews - not over 5 million.
The "real-time" nature of the reviews was also challenged, as the company could not or would explain how they analyzed reviews and created star rankings in real-time.
Skytrax was not able to substantiate any claims to being the "official quality star ranking" for airlines, despite claiming to have an agreement with all involved parties. In addition, the claims to trademarks were not verifiable, suggesting that these marks were not protected as claimed.
A Skytrax spokesperson has responded to a request for comment, stating that "the ASA ruling and comments about the Official Skytrax Star Ranking was overturned this week, you will see that is (or has been) being reinstated across all of the relevant parts of the web site."
Skytrax also points out the reason ASA asked Skytrax to change the wording was quoted as: because Skytrax deleted user information soon after receiving a submission, they were not able to provide evidence demonstrating that the reviews which existed on the site at the time of the complaint had been subjected to, and passed, that procedure."
Skytrax now seems to have removed all mentions of "checked and trusted" from the site, and appears to be complying with ASA's ruling to "not to imply that the reviews on their site were checked, trusted and genuine unless they could provide substantiation to that effect."
Skytrax has also renamed their airline and airport ranking product the "Official SKYTRAX Airline Star Ranking" and the "Offical SKYTRAX Airport Product and Service Quality Ranking," respectively.
Skytrax had a full response to the complaint posted on the "News" section of their website, which stated the following by Skytrax's Edward Plaisted:

We have never been accused of posting false or defamatory reviews, and all user created content featured on our websites has been checked and authenticated by our in-house, website staff. With over 1400 airlines and airports featured on our website, not one of these companies has ever complained about user reviews being false, defamatory or unfair. That in itself underlines some doubtful, self-serving commercial interests at play when a self-appointed critic of review sites attempts to undermine confidence in a proven and established user forum. Had we received complaints from our users, an airline or airport, it would of course have been treated with more seriousness.
Chris Emmins of KwikChex believes that the verification process for user reviews is essential not only for trust, but also for a fair and functioning small business environment.

"The effect of fake reviews is variable in terms of both consumers and businesses. We have seen exceptional abuse of posting fake reviews that unquestionably make businesses appear better than they are. Some rogue businesses have used review resources to successfully dupe consumers and push their false positive profiles high up search engines. We often flag such instances to the sites, the authorities and Google. Fake negative reviews can be particularly devastating to small businesses."
For websites and businesses looking to offer user-generated reviews, Emmins offers the following suggestions to ensure that the system remains fair and balanced towards true and authentic reviews.

"There are a number of steps that would help reliability. All are based on aspects of authentication.
On TripAdvisor, business owners are asked to provide credit card details to verify their identity. Many businesses feel that such a system should be applied to reviewers.
Other additional authentication options are to confirm by text (the reviewer provides a mobile number and has to reply to a text from the review site).
We are also suggesting to reviews sites that they encourage reviewers to state whether they have proof of purchase - this could then be provided to the reviews site if a challenge of a fake review is made.
No system will be perfect and there will always be the possibility of distortion, but given the extremely influential nature of reviews, and the ease of abuse, all authentication steps help protect consumers and reputable businesses."
KwikChex previously filed a complaint against TripAdvisor for implying that all review content was genuine. This complaint was also upheld by the ASA, forcing TripAdvisor to alter copy relating to the authenticity of their on-site reviews.