Yes Man also didn't have to "obey" anyone's orders as I understood it. He just has to tell people whatever they asked of him - he was an "answer" machine. You ask, he answers. Notice that on most occasions, he's the one telling YOU what to do.
He's not telling you to do anything. He's only making suggestions based on the plans of Mr. House. You can tell him no to destroying the Brotherhood, for example, despite them being the greatest threat. He has no ability to command.
If you were really in charge at the end, the bit about him becoming more assertive would be unnecessary as it flows against that narrative. I mean, why would they end the game on such a trivial detail unless it had greater meaning?
You were in charge. Him becoming assertive lets him take charge. That's not trivial. If Yes Man doesn't take charge then anyone on the strip could start bossing him around while the courier goes off to further adventures.