Frames are, of course, just an abstraction, not actual discrete entities. Another way of understanding it is to think of your frame as a linear combination of other frames. If two or more heavily weighted frames are in conflict, as they were in your case, then there's going to be some stress.

From your description, it sounds as though you actually switched frames at work from that of an idealist trying to do the best possible job, to that of a cynic who just plays along with a system you don't respect. This new frame is more compatible with your startup frame, since it understands that stupidity of large organizations creates opportunities for startups to succeed.