Nitwits usually do.
As to your earlier point, that Annika is depriving some "deserving" second-stringer of food and clothing, is simply wrong -- a tournament sponsor can give out exemptions to anyone they please. And it pleases them to give one to Annika. So rant on, for all the good it'll do.
Apply this same advice to your comment about the 5-iron and putter. What kind of score do you think your 100 buddies who need a sponsor's exemption in order to get into a PGA tournament would post through two days of playing from the championship tees on a course like Colonial? 8 under? 5 under? even par? Not likely.
From what I've heard, Annika's short game is comparable to an average player on the PGA tour, but her putting is very good. I think it will be interesting to see how she fares against the men on the tour. I guess every guy that she beats will probably think "Wow, I guess I should have just brought my 5-iron and my putter instead of all 14 clubs."
You are the one without a clue. According to my sister-in-law, who is a top executive with one of the major sponsors on the PGA, Senior PGA, and LPGA, the sponsor can hand out something like four exemptions to just about anyone they want (the other four go to active touring pros who are otherwise not qualified). In most cases, the sponsor gives the exemption to either top ranked amateurs (like Tiger before he went pro or that 16 year old kid we have seen of late) or has beens, who have served the sponsor well over the years (can you say Jack, Arnie, Lee, and Gary?).