A lot of instructors are not all that clued-up. My main PPL instructor said a VOR (not a DME) stops working if too many planes tune into it, because the transmitter sends out a special signal which sets up the TO/FROM flags.
The full explanation of how the flags are driven is actually fairly complicated (to a non-electronics person) so this kind of crap is not implausible unless you know better.
What gets up my nose however is how many people are simply non-transponding. I flew for 2.5 hours today, in the south east, and got a traffic service about 75% of the time. Not one of the 30-50 or so contacts was transponding.
The cloudbase was generally 800-1500ft AGL and the tops were 3000-4000ft. I was VMC on top and worked around the LTMA to stay there, because there was quite a bit of ice in the cloud below (temp -2C, against +3C above under the blue skies).
I don't think they were gliders, either...