Thats how it recall the documentaries about it. The controller gave conflicting advice, the russian pilots followed it, and flew into the path of the other aircraft that had avoided them.
There's a reason why the rules are "if the controller says something different to the TCAS, you follow the TCAS".
As an aside, the reason why avoidance action is always given as ascend/descend is simply because the vertical axis (height) is the most accurate - there's much less accuracy in position and heading although modern GPS systems have probably improved that significantly. When TCAS was being developed, the only really reliable information is the heigh information provided by the other aircraft in the vicinity - the horizontal position being (originally) "fairly vague" based on radio bearing (crude measurement) and signal strength (crude proxy for distance).
The choice of who climbs and who descends is by fixed rules (who's got the higher transponder code) so unless there are bugs in the software, you'd never get two aircraft being given the same advisory.
But as has been pointed out, the aviation space is relatively benign. Once in controlled airspace (particularly Class A where equipment and qualification requirements are fairly tight), you don't need to worry about pedestrians, kids on bikes, pets dogs, cattle, ... There is still the issue of (typically) light aircraft without all the hi-tech (and expensive) TCAS gear, but even then it takes some effort to get two aircraft very close - hence why we insist on herding them into smaller areas around airports and into airways to justify the effort of keeping them apart :-)
So given that there will probably never be 100% "clever" cars with all the comms gizmos, and we'll always have other road users (people, animals, stuff that's fallen off things, ...), autopilots for cars are always going to be quite a lot harder to implement. I look forward to when they start properly throwing them into urban environements - that's going to be a lot of fun for other drivers who know how to "game" the automation ;-)