I think they all become collar-wise. They know they've got that thing on their necks, and they sense the rules are differently enforced in its presence. What we control is the level to which they are sensitized to that fact. And you don't hear this often, but being collar-wise isn't necessarily bad. WHAT??? Okay, here's what I mean by all that.
Dogs are situational learners. That's painting with a broad brush. But it's accurate, and applies many ways to dog training. Just as they are sensitive to triggers in their environment that tells them they're at a trial today, (or test, or hunting, etc), they also are aware of the tools we use in training. What's the difference between a dog that is fully aware of the heeling stick a trainer is holding, and one that is stick-shy? Inappropriate, or inconsistent standards of application, don't you think?
As to the e-collar, gdgnyc made an important point about not giving commands when you aren't in a position to enforce them. If you have e-collar conditioned your dog, and you're going training, the collar should be on the dog. If you're going out in the yard, and plan to let your dog run free in a fenced yard, it's optional because enforcing commands in that close environment is easy, and can be done without the collar. We have other tools. Besides, your dog should be well trained enough that correcting him all the time should not be a consideration. When we discuss these topics it's easy to get the impression that they never obey unless we're nailing them with some forcing implement.
When "collar-wise" exists in a destructive form the dog behaves compeletly different...is obedient with, and totally disobedient without the collar. That happened because someone put the dog in positions where commands were given; sometimes with the collar to enforce them, and sometimes without it. What's the trigger? The presence of the collar, or the absence of it.
I used to train with a nice guy who just could not stay off the button. If he blew a sit whistle, there was a nick with it. His dogs would get 'buggy' over time. His first reaction was to put the transmitter in his back pocket. That didn't work, of course. The first mistake his dog made and he played Quick-draw McGraw with that transmitter! Then he decided to run his dog without a collar on as his last ditch effort at self control. What do you suppose was the result of that?