This is absolutely incorrect. Valve puts up with Uplay because they aren't a competing marketplace, but when EA wanted to make their new games sold on Steam require Origin installation as well, Valve told them to go fly a kite. That's why games like Battlefield 3 are not available on Steam at all.

Judging from Steam forums it seems that they are mostly Origin-free and do not chain DRM schemes like it was the case with U-play.

Some may require "EA activation" which pops up at the first run of the game, but they don't require origin if they have a Steam key.