Slightly off topic, but I notice that the original "scary story" actually had the two aircraft 1.8 nm apart at their closest point.
I know I probably need a new prescription for my spectacles, but without a contrail, and with some ground clutter in the background, I suspect I would never have even seen someone nearly two miles away, let alone worried about hitting them.
Since TCAS issued an RA for this one, I would deduce that (1) the advised climb was probably quite modest and (2) that TCAS is fairly conservative.