Screening Player Characters
Player character creation is the most important step of your game. It is more important than any NPC you have prepared or any plot you have in mind. Decisions made during PC creation will determine the entire outcome of the game. I really can't stress how important it is. Good character creation stacks the deck heavily towards a good game, and bad character creation does just the opposite.
If you carefully screen PCs during the creation process, you can relax control during play. You can give the players free rein to do whatever they want because you have already set the boundaries and agreed on them.
What's the alternative? You let in characters that can do things you don't want them to do, or who have personalities that you don't like. You vaguely hope the players won't play their characters as written and wreck the game you have in mind (“sure she can speak with dead, but maybe she just won't talk to the murder victim, because that would be a short mystery”). Which is entirely unfair to the players, because when they do play effectively you are going to hold it against them instead of rewarding them. You are being dishonest in approving the characters in the first place. The player may not even realize they are wrecking the game until it is too late.
Common wisdom is that NPCs are the domain of the GM and that PCs are the domain of the players. The GM prepares the game, the challenges, the skeleton of a plot, and the players bring the protagonists and cope with all the stuff you came up with, boldly forging their own destiny out of the chaos.
Character creation is the first contribution players bring to the game, while the GM has probably been hard at work for days (or weeks, or months) in advance. Which should tell you something right there: the GM knows more than the players do. The GM knows what kind of a game is in store, at least in vague optimistic terms. Therefore the GM has a better sense about what kind of characters will work, and what kind of characters will take all the fun out of the game. You can reveal some of those criteria, but it's impossible to list everything that _won't_ work without revealing too much about the game (“err, ah, no you can't have protection from vampires. No reason.”).
The players start off owning nothing except their characters. There is no shared experience until play starts. This can lead to players only thinking in terms of what they want to play, not how it will work with the other PCs (which is why group character creation can be such a big help). On the other hand the GM is looking at the big picture, the group as a whole. The GM is biased towards making sure the characters fit the game, but that's good because it serves everyone's purposes.
Are you stepping on player's toes by getting involved in the character creation process? It may seem that way, but the goal is to play a game together not have players make their ideal characters — they can do that at home at their kitchen table. You could give each player everything they wanted during character creation, indulge every possible whim, and they would be happy right up until they started playing and everything was too easy or just a bad fit.
When you reject a character that is going to wreck the game you are doing your job of making sure everyone has a shot at having a good time. You are doing the other players a favor, and more often than not you're doing a favor for the player with the trouble character too. Players have to like their characters to enjoy the game, but in the end they will have more fun with a character that fits.