Consider the Ueberlingen scenario with a slight modification: The Tuplolev has, as allowed for dispatch, an unserviceable TCAS system, but fully working transponder.
Yes...
the DHL Boeing gets a resolution advisory, but the Tupolev gets none. The Tupolev does get, however, a manoevering instruction from ATC ("descend FL350 expedite", iirc). The difference here being between not following an RA versus not getting it. Educate me about TCAS: would the DHL crew have known about the Baskirian's TCAS being inoperable?
Would the DHL crew know about the other aircraft's TCAS? No, unless they'd been told about it.
Would the DHL aircraft's TCAS know about this? Yes. It would treat the Tu-154 as a "dumb" target and expect to be doing all the manoeuvring whilst tracking it.
If two or more TCAS equipped aircraft come into conflict with each other there may be an element of
coordination between the TCAS units to decide who does what; e.g. "You go up, I'll go down". This is what makes manoeuvring
against an RA potentially serious as other aircraft may have begun to manoeuvre in
expectation of a certain manoeuvre from you. It's a bit like indicating left on a busy road then suddenly turning right.