That would be true if you're thinking of Stadia as a subscription to get access to an all you can eat buffet of games (ie Netflix for games) but that's not the primary model proposed. The primary Stadia purchase model is that you buy games on Stadia and then get "free" unlimited streaming of them. In that case if they were to shutdown the user has to get something back, preferably the game...
That's beside the point, though—my reply, it's parent and it's grandparent were discussing Google products generally, not Stadia specifically.
[0] I realize that Takeout doesn't support Stadia. Though, for two different Stadia titles (Destiny 2's "cross-play" and NBA2K20's "MyPlayer"), I was prompted to log into a publisher account where my data could be linked/stored or something.