I twitter for personal. As a business owner myself, I wouldn't mind if my employees were on Twitter, but I'm in the design business and create web sites. We're online all day anyway. I can see if you had one person who ended up twittering all day and not getting any work done or writing about inappropriate things. It just takes one bad apple to ruin it for everyone else right?
Sounds like this might be a deal breaker for you. Good luck with your decision:-)
SInce I'm self-employed and my name and my community is part of my brand .. I blog about personal things as well as "business related " things too. I know the boss doesn't care about it because I'm the boss. : )