I gotta say, I think their definition of encounter (in the context of the Factotum, at least) makes perfect sense. I can't think of any cases off the top of my head which wouldn't work, regardless of whether a Factotum's involved or not, and I think that the Factotum makes a perfect example of why an encounter needs to be codified.
Granted, you need to use a little common sense. For example, if they're trying to break down a door and fail, if they wait a few minutes and then try again, it shouldn't be treated as a new encounter. The door is a single encounter. In fact, I'd go so far as to say that if they try to break down a door, fail, go somewhere else and have some combat, then come back to that door 5 hours later, it should be the same encounter. In essence, things limited to so many uses per encounter would be how many times you could use them to take a whack at a particular problem.