XCom rookies are good, but like others said, I don't think they are the best of the best. I think the countries sending them may tell XCom they are the "best of the best", in much the same way they assure us that they are giving us "as much funding as they can possibly afford". But seriously, I don't think the countries of the world take X-Com seriously (at least at first), and they are only going along grudgingly until they see some actual results.
I actually imagined XCom had its own recruiting agency as well, and didn't just limit itself to those "offered" by the other various countries.
I'm in agreement with this, but on top of this, I think that while X-Com personnel and the overall organization gives an air of people who have no training and absolutely no idea what they're going up against, I think they made the alien threat a bit too serious. Not in that it's too dangerous, but that the Alien threat is a threat at all given that you can handle them with a group of utterly incompetent draftees.
There seems to be an element missing from this, in that the alien threat isn't really all that threatening in the first place and our information as the players might be false justifications and inflation of the dangers the aliens pose, both through doctored media and sending green horns that haven't held a gun before to get slaughtered to fabricate a plausible excuse to receive more UN funding.
If it were this case, I'd find it believable given the abysmal performances of the soldiers given to this program. Personally, if aliens were invading I'd imagine a much bigger reaction from the collective world communities and far better equipment than what is given to XCOM personnel.