I didn’t dig in deeply, so I can’t say, but it’s either the official backup method generates an SQL dump that doesn’t work, or importing it causes a showstopper failure that didn’t have to be a showstopper, or the database has been corrupt for years but Postgres just keeps running anyhow if you rsync it over.
In theory, SQL indexes are just for speeding up queries, right? So it’s possible that the rsync’d system is just disregarding it and something is suboptimal in some small way that we haven’t noticed. I really don’t know.
Chatter on other threads suggests that some version of Postgres broke things, and a later version fixed it, but I don’t know the specific technical details of what went wrong.