Your instructor is wrong, there's nothing that prohibits filing an IFR
direct route regardless of the status of your nav equipment. Whether or not
the controller can clear you on such a route depends upon radar coverage,
but if he can clear you direct once you're airborne he can also clear you
direct when you're still on the ground.

On the first day private flying was permitted after 9-11, I filed
direct from Rutland VT to Bloomsburg PA , about 250 miles, with "VFR
GPS in "remarks," and got it! I was quite surprised, but perhaps the
fact that there was extremely little traffic that day had something to
do with it.

But for many years, before GPS or even RNAV, I filed direct from UNV
(central PA) to MAPEL (about 100 miles) direct Dulles, and usually got
it.

I was never asked how I could do it. (I had noticed that the radial
out of IAD (Dulles) that went through MAPEL also went through UNV.)

Direct LISON Direct DCA also worked, for similar reason.

vince norris