Essentially? It's your game and therefore you have every right to tell someone that you have problems with their CS. Your post makes it sound as if you're hesitant to present yourself with any sort of authority - but you [i]do[/i] have authority. And if you feel the need to make a decision for the good of your RP then, by all means, make that decision. 

Of course I would advise you to be polite about it, pointing out specifically which parts are unacceptable and why, and potentially help the player fix up their CS if they're willing to work with you on that. (Fair warning: every once in a while you'll find a person who'll refuse to accept that there's anything wrong with their character and throw a fit when you confront them about it. Feel free to just strictly kick out anyone being uncooperative like that - they're at fault, not you, and your RP will be much better off if you get rid of them early.) 

But yeah, you just sound like you're hesitant to say anything. But so long as you're polite and reasonable, you should have nothing to worry about. At least 95% of the people here will respect your decision and most will probably be willing to work with you to fix whatever flaws you had to reject the original version for. Just don't be afraid to act as a GM and you should be fine.