> Unless they're full puppets for foreign interests,

The European parliament has been bought 10 times over by the lobbies.

See https://www.theguardian.com/world/2014/may/08/lobbyists-euro...

"By some estimates, they influence 75% of legislation"

> But even then, they could not have possibly been all mere puppets. And yet.

Even if the lobbying was not reason for all the bad decisions of the EU, the EU parliament has no way to actually propose any laws on its own. All the laws emanate from the commission which is also bought and paid for by you guessed it, the lobbies.