"Chip Jones" wrote
The trainee and I did discuss where the "full approach" began. Since we
rarely work aircraft approaching RKW from the east, it was a legitimate
question in my mind.

Chip, I'm honestly not trying to be a pain, but while the question was
a legitimate one in your mind, it wasn't legitimate regulatorily. In
other words, I think the source of the confusion is a less-than-ideal
understanding of the applicable rules. Don't feel too bad - I just
saw the same level of understanding in a 1500+ hour multi/IFR pilot I
flew with recently.

This aircraft had GPS, so I said
I though the full approach in this case begins at the IAF (MINES)

The full approach ALWAYS begins at the IAF (or an IAF if there is more
than one) regardless of how the aircraft is equipped.

and we could clear him to MINES via GPS-direct.

There's the difference. Since the aircraft had RNAV (not necessarily
GPS - any kind of approved RNAV would be fine, since the approach does
not start until the IAF is crossed) you could clear him direct to
MINES. Without RNAV, you would need an alternate plan.

The trainee thought that the
"full" approach began at HCH Vor

Well, he was wrong - but as a trainee he has every right to be wrong.

Now I'm wondering what I could have done with this UH-60 if it had been a /A
instead of a /G. We don't clear /A's direct to intersections. Where does
the "full approach" begin for a non-RNAV on this procedure. I can't vector
to final at this location.

I'm pretty sure you can vector an aircraft to intercept an airway -
can you do the same for a random VOR radial? How about "Fly heading
XXX, intercept the HCH-060 radial, track the radial to MINES, cleared
for the full approach, report procedure turn inbound?"

Michael