Wow, this place isn't as friendly as it used to be!
TCAS does display traffic around you though doesn't it? I was trying to get across that these are only diplayed in 12 'sectors' of 30 degrees so it is quite possible that traffic showing on your display at half past 11 could easily be half past 12 and a turn to the right would be a bad thing.
I do know even if you are visual you should still follow the RA but it must be very tempting to make a turn to avoid. Hence the "turn to the right might work" quote.
It's a shame this forum has turned into the place it has. I've learnt so much from it in the past but now it seems posters would much rather flame others than give them the benefit of the doubt.