I can see why you would want this... IMO, this isn't really needed. Maybe there are some cases that it would be handy, but it would lead to problems (impersonations of highly respected groups, etc.) and personally, I think that not many users would do it. Look around; do you see many people that are part of a group? Not really.
If it was to be implemented, I'd say at least get rid of the trust rating sum thing. I don't see much of a use for it and it could be taken advantage of (a potential scammer finding his way into a group with a high accumulated trust rating, and then using that to scam people without the need to get those DT trust points and wait a while).