At a lot of airports, most of the people on the headsets during the push-backs are ground handlers, not engineers. They would have basic aircraft handling knowledge and are not qualified to offer technical advice to pilots.
Those that are qualified and on headsets might be asked with a technical question if there was a failure during start-up. But the engineer in question would only be able to offer advice on experience alone. Anyone who offers a solution without consulting maintenance publications exposes themself for liability. Don't forget that the CVR records what is said on the intercom.
Your students should be briefed to advise the pilot to consult either the ramp line office or maintrol in the event of any failures, so that qualified staff with the appropriate publications can advise. It's not fair to put the onus on the guy on the headset just becuse he the nearest and easiest to contact.