Now I'm not an airline pilot, and my aircraft doesn't have TCAS - I wish it did, but that's the defence budget for you.
But to me, all that those examples from Eurocontrol demonstrate is that the aircrew did not understand the sole condition for a collision, which is that the target is closing on a constant bearing. This is, incidentally, why see-and-avoid is a poor answer in VMC. The target that's going to hit you is stationary in your field of view (if its in your field of view at all), and evolution has equipped us with a visual system that responds best to movement (it picks up the twitching grass as the sabre-toothed tiger crawls up on you). Change any part of the dynamics and the collision is avoided. For well-thought-out reasons, TCAS uses the vertical as the avoidance dynamic. But on any contact, if the bearing is changing towards the 12 o'clock, the target will pass ahead, and if the bearing is changing towards the 6 o'clock, the target will pass behind.
Sorry if I'm teaching granny to suck eggs.
Sven