I know this has already gotten the check-mark, but I feel like there's a bit more to contribute.
Short answer: Yes.
Long answer: Robusto's answer is correct, but take note that the NYT article is from 2007, when the controversy about the show initially erupted. It's all well described in the Wikipedia article, but the gist of it is that the show initially was edited to make it look like Grylls did everything on his own. When it was discovered this wasn't the case, Discovery channel apologized, re-edited older episodes to clarify when he gets help, and the show has for years now had a disclaimer stating that he gets help from his crew. So yes, he receives help from his crew when his game traps fail (most of the time, it seems), when extra equipment is needed, or to just go to sleep at a hotel somewhere. The disclaimer also states that he puts himself into situations you could probably avoid in order to show survival tactics... but that's kind of the point, isn't it?
Few people probably genuinely watch this show to learn how to survive; they want to be entertained, and Grylls knows that. So if his crew provides him with a rabbit or a harness or helps him make a tree shelter, does that really matter? Does that actively take away from the end result? I suppose it did when the show had the pretense of being "real," but it dropped that years ago. Now his crew is just helping him get into and out of trouble, and that's entirely what makes the show fun. It's staged, sure, but being staged doesn't mean Grylls didn't actually just hop into some peat-pit for no reason, or didn't just scale a mesa without any ropes.
One final comment: according to his own Wikipedia article, his birth name isn't Humphrey, it's Edward. (Not that it matters.) And the name Bear comes from a nickname his sister gave him as a child. He's a legitimate climber, though: he's scaled Everest. Check out the page to see some of the other kinda ridiculous things he's done.