Well, I think the connection is to do with something being surprisingly true, in particular with reference to time.
still: It's surprising that it's true now; we would have expected it to be no longer true.
yet: We are surprised that it is true now; we expected it to be true in the future.
even: We are surprised that it is true to the extent that it currently is. We expected it to be true, but to a lesser extent.
Note that I think "even" is more usually translated with the expression "til og med" - the picture here is "everything up to and including..."
Someone should fire that male voice; he mumbles! :-) He says "De er" and "De har" exactly the same. I kept hearing this as "De er ikke barnet nå" (which makes little sense). I had to play the slow version to hear it right. On the other hand, the female voice (above) is delightfully clear!