As far as I know, ATC is not automatically informed about TCAS resolutions. Therefore, the phrase "TCAS climb/descent" is usually issued by the affected pilots to clarify their actions.
The problem with disaccording instructions is the response time of TCAS (45 sec TA, 20-30 sec RA) plus the usual time lag in RT communications.
ATC might just have worked out some own way to resolve the situation when at the same time TCAS issues a different instruction.
So there's ATC telling you to descend and your TCAS telling you to climb (that's what happened in germany). Since both do not know of the other, you have to choose... and since TCAS' informations are usually more up to date (up to second would better describe it) plus TCAS issues coordinated (with the system of the other aircraft) resolutions only, it's always my choice.