Seeing a service like this makes me wonder if Postgres could support encrypted replication. That would allow using a service like this to provide reliable backup without having to trust it with customer data.
It's technically rather challenging, but when enough users would ask for it, I know putting some resources into it might be viable.
Just stream the WAL in an encrypted format, and store it there? Easy enough. But that'll mean that it'll potentially take a long time to re-apply all those changes to a base backup.
Actually apply the changes, even though the database and WAL in encrypted? Unlikely, don't really see how that'd be possible. And even if, I'd bet that it'd be fairly easy to generate compression type attacks.
The backup wouldn't actually be particularly useful though. So I'm not really sure what the use-case here is.