That Claude support page says the exact same thing about AWS (“retained data stays in your AWS environment”). AWS’s docs say differently, though, so it seems one of them has incorrect documentation. I wouldn’t necessarily trust the Claude docs to be correct even regarding GCP until some of this is ironed out.

edit: Google’s own docs also say zero data retention isn’t possible with Fable and your data will be retained for 60 days “outside of your account”. I’m doubtful that this data sharing is an AWS-only thing.