Brett,
I think you asked a much better question than the answers that you got. Here are two hypothetical scenarios that might happen under part 91 ops:
1. You're participating in a formation flight for the purposes of a photo shoot. Everything is thoroughly briefed and legal, but during the rejoin, you forgot to turn the TCAS from TA/RA to TA Only, and you get an RA. Both pilots involved have good visibility & situational awareness and there is no risk of a collision, but you have an RA. Are you *required* by part 91 to respond to it?
2. You're descending at the speed of heat, speedbrakes out, down to 10,000 to make a crossing restriction. You can see that you'll make it, but only just. ATC calls traffic to you level at 12 o'clock and 9000'. You report him in sight, and he likewise acknowledges you in sight (and was told that you would be leveling off one thousand feet above him). No other traffic nearby. Just before the autopilot begins its level-off, you get a "climb" RA. (Perhaps the traffic gets a "descend" RA.) You know that unless the autopilot botches the level-off, there will be no risk of a collision (and if it does, then you'll have time to disengage it & maneuver to avoid the collision). Does part 91 *require* that you intervene and respond to the RA?
In the part 121 FOM at my job, we do NOT have the option... we must respond to an RA. End of discussion. (Sure, you always have the *ability* not to respond, but you'd better have a good explanation, in terms of captain's emergency authority, avoiding a worse threat, whatever.) Of course, we don't do photo shoots, and we're told that the current version of our TCAS software won't flag cases like my (#2) until you MUST take action.
I think Brett's question is a valid one, and I'm not smart enough on Part 91 to answer it. Does Part 91 *require* a response to an RA in situations like those above? Or is it simply a really, really good idea 95% of the time, but technically the pilot's option?