To me the ability to recognize intervals, hear what chords should go where, and what the chord progression is is one thing.. tuning is another. I learned tuning very quickly, but the other one took me about thirty years of guitar playing to start getting anywhere.
I have never used, or even seen a pitch pipe, but.. do they sustain? One of the great things about using a tuning fork is that it rings out, so that you can hear the beat note between the ringing string and the ringing fork, and then it's purely a mechanical job to tune the string correctly - at least if you first get the string to be somewhere in the right area to start with. And then tune the other strings against the first one by pressing frets here and there. If it's difficult to hear if your string is above or below then just bend it a bit, either the beat note increases its beat frequency or it drops, and that tell you which way to tune.