I think what tastytea is saying is that when emacs checks the env
variable COLORTERM, it uses the environment of the server and not the
one of emacsclient. And yes, that's just a bug. emacsclient should read
that variable and pass it to server. But this requires new code because
it breaks with the pattern of using terminfo to detect term support.

So the terminfo detection is currently more reliable. Would you be
willing to accept something like the attached patch? This will improve
detection without relying on COLORTERM, which should make the situation
already much better. Tc is in the terminfo of many terminals, see
https://gist.github.com/XVilka/8346728 .

If yes, I can send an improved patch (with added explanations to
doc/misc/efaq.texi).

Tim