They’ve already had an “unused clip show” of the U.S. version, most notably featuring Ryan Stiles singing three or four different hoedowns that always seemed to end up being about the girl whose underwear got shown on national television during that episode.
That might give some evidence that it is actual improv. Some other clues are Questions Only (if it was rehearsed, nobody would get it wrong), the little things that go wrong (Ryan bumping his head into Drew’s desk), the audience participation (which I saw at a Wayne Brady show, so it’s not faked), and Drew’s giggling.
Why are they so good at it that some people think they’re faking? One word: Practice. For example, Colin was absolutely horrible at hoedowns, doing everything he could to not have to sing too much (“he really, really, really, really, really, really did” to falling down “dead” before the last line), but after several years, he’s gotten pretty good. Also, Drew is improving, at least in the hoedown area. He had the same Colin Mochery syndrome and when he actually completed a hoedown that not only made sense but was funny, the audience was stunned.
Why do some people hate it? Well, some people hate Drew Carey or some of the performers just because they rub them the wrong way or whatever. Some people just find the humor too unsophisticated and, being the snobs they are, despise everything unsophisticated (although the first few seasons of the British version were pretty high up there). Also, there are minor flaws in the show, stagnation shows up from time to time, and people just don’t always find it entertaining. However, these last few reasons usually simply lead to not liking/enjoying the show, rather than hating it.
The only major thing that bugs me about the show is when major celebs show up and try and move outside of the confines of the show (e.g. Robin Williams), in order to try and steal it. You can almost see the frustration on the other players’ faces as their thinking to themselves, “Come on, just play along! Don’t do it ‘your way’!”