Your instructor is correct.
Let me quote some advice from the Australian Bureau of Meteorology: "St. Elmo's Fire - as visible evidence of electrical discharge at a tolerably slow rate, this is not a problem, does not cause any form of damage, and in fact serves in a positive sense as a warning that the enviroment is electrified, and lightning may possibly occur."
If you do experience St. Elmo's Fire inflight, you should have the aircraft prepared for both lightning and turbulence. Cockpit lighting turned up, crew and passengers with seat belts fastened, ignition on, engine anti-icing on etc.