Jennifer Aniston has ever said that Meg Ryan faked her Actor's Guild card. The YouTube video you linked to is a fake. The video description says that it is a "spoof" and that the actors in the video are not Jennifer Aniston and Meg Ryan.
The rumor that Meg Ryan faked her Actor's Guild card has been circulating online for many years, but there is no evidence to support it. The rumor appears to have originated from a 2004 article in the National Enquirer, which claimed that Ryan had been caught using a fake SAG card to audition for roles. However, the Enquirer's source for this claim was anonymous, and Ryan has denied the allegation.
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It is possible that Ryan did once use a fake SAG card, but there is no proof of this. The rumor is likely based on Ryan's reputation for being difficult to work with. She has been accused of being demanding and diva-like, and she has been known to walk off sets. It is possible that some people have spread the rumor that she faked her SAG card as a way to discredit her.
In conclusion, there is no evidence that Jennifer Aniston has ever said that Meg Ryan faked her Actor's Guild card. The rumor that Ryan faked her SAG card is likely based on her reputation for being difficult to work with.