Here's how I remember it:
1. Team is playing better without Ray;
2. Subject of Ray being benched comes up;
3. Ray at first makes a strange quote, something along the lines of "If it will make the team's offense better, then yeah, I'll go to the bench".
4. Fans start clamoring very loudly for Bradley to start;
5. Doc indicates that Ray is fine with coming off the bench.
My thought at the time was that Ray never wanted to come off the bench -- thus, the "if it helps the *offense*" line -- and wasn't particularly happy about being benched, but he tried to be a good soldier.
EDIT: Here's Ray's quote at the time:
For his part, Allen says he would graciously accept such a move if coach Doc Rivers sees fit.
“If it makes us better offensively, I have no problem with it,” Allen said.
I always thought that was strange, and wondered if it suggested that the benching wasn't as willing as was being reported. The flip side is perhaps Ray was suggesting that the entire offense would be better if he was the 6th man, but that's never how I read it.