NigelOnDraft
Firstly, I think that the accident you refer to was one where the crew ignored their TCAS advisory and acted on ATC orders instead (and hit the other plane). So this is hardly a case of TCAS "causing" a crash.
Secondly, the altitude information fed to the TCAS in your airliner is also from a barometric source. No different to the GA systems such as
this one.
The system is informational only - you don't get resolution advisories. But it does tell you about where other traffic is in both azimuth and relative altitude, so the resolution is obvious. In a head-on situation, you turn to the right, etc.