P Staney
in answer to your query - you are correct.... ATCOs would not ask you to switch off mode C unless it was malfunctioning.
We get lots of nuisance RAs, even when we tell both sets of aircrew that they are climbig/descending to within 1000' and they slow their rate.
It's one of those things unfortunately, it would be nice if TCAS evolved so that it could interrogate the FMS of the intruder and if it then knew it was levelling off above or below, it would not give a warning (but it would have to continuously monitor the intentions, as a further climb/descent may have been given in error since it last checked!!)
All gets a bit complicated. The main thing to bear in mind is that pilots must comply with RAs then let ATC know when they are back under their control. Pilots should never second guess TCAS. And TCAS displays should never, ever be used as a pseudo radar by pilots who then may (it has been known) turn in the misbelief that they know what is going on!!