Its good to see that everyone seems to speak the same language. There are some "cultures" however that still seem to prefer ATC instructions above TCAS instructions. This has been a very extensive topic of discussion during the investigation of the swiss midair. Cockpit recordings have shown that the crew of the russian airliner were in dissagreement with each other re this topic.
The comment I made regarding that a "good" (and I hate to use the word good) ATC should/could add "TCAS has priority", is off course only in the case where uncertainty exists to the ATC, on whether a RA has been given by the TCAS.
You are quite correct in saying that if any of the pilots have reported a TCAS descend/climb, ATC should do nothing, and let the TCAS do its work.
I have been part of an investigation (after the swiss midair), where the ATC was involved in a reduction in seperation with a CL60 and a B732 head-on at FL350, and after noticing the conflict, the ATC instructed the CL60 to descend immidiately, after which the B732 reported that they were already on a TCAS descend. Luckily nothing happened, but in this case it would've been helpful to add "TCAS is priority, descend...) A Few seconds hesitation by any of the crew could be fatal in such a case.