No, the publisher CAN have a say in what happens in a game. Usually they sign contracts with development studios and they own the entire IP. An example would be Ratchet & Clank with Sony and Insomniac. Sony owns the IP even though it was internally created at Insomniac.

So while a publisher owns an IP, they DO have a voice in what happens to a game, since they technically own it. While a studio is working on it the publisher can come in and say "You need to remove some complexity to make it more accessible to the larger market. You need to add a multiplayer mode. You can't do that? We'll bring another studio in to tack it on separately." That's just a possibility when someone else is paying you to make the game. Good publishers know and trust the companies who make the games and don't bother them, but you'd be surprised how much it actually does happen all the time.

A company like Valve on the other hand, is privately owned and self-publishes (but actually works with EA on distributing, ironically). So they never have to answer to a board of directors or any stock-holders, which is why they can operate on their "release when we want to" schedule.

tl;dr Publishers do dictate how certain games are made, for good or ill.