BPF, have you ever flown a SLPC aircraft? Although their operation is indeed very simple if all is well, the failure modes and thus the associated emergency drills are completely different from your conventional Lycosaurus.
The authorized emergency/abnormal checklists for our clubs avgas burning aircraft is one column on an A5 sheet, while the same checklist for the DA-40 TDI runs for two A4 pages. Admittedly that's probably a bit overkill but it was the first diesel in our fleet and they wanted to be thorough. Still, at least one possible failure scenario was not covered in that checklist, almost causing a mate of mine to overshoot his emergency power off landing because the engine all of a sudden went from 0% to 100% power, apparently uncommanded. Quick thinking and quick reactions saved the day, fortunately.
So yes, as far as I'm concerned, differences training is a justified requirement, with an emphasis on failure modes and emergency scenarios.