Incidentally, a rather nasty TCAS incident is often quoted in my company, in which one a/c received a 'Climb' RA in response to a threat above it. (Both a/c were changing levels!) The crew of that same a/c saw fit, on the basis of visual acquisition, to 'manage' the demanded manoeuvre!
Forgive me 4468, but I'm not following what happened.
By 'managed' you mean that they decide to ignore the RA and stayed level? And that led to a tighter conflict, near collision? Presumably that was because the other a/c was already descending and TCAS was telling it to descend assuming our protagonists were going to climb as directed?