A while ago I read a review of the DA42 and the reviewer expressing the opinion that the thing was so easy to fly assymetric that an ME rating done it in "should not" be valid in more conventional types, but I am not aware this has ever become law.
(Some of LASORS is law, AIUI, for areas of regulation that have been delegated to the CAA).
Same with the avionics. A G1000 is no more complex than a GNS530 integrated with the engine instruments. It isn't an FMS. It will have plenty of gotchas (I have no experience with it myself) but every IFR GPS has plenty of gotchas, and then a whole lot more when it comes to integration (or lack of) with the autopilot, the HSI, etc etc. But there is no law requiring diff training for any of this.
I would ask for references.
Club rules are something else, of course. Anything goes in club rules. They can require you to wear two pairs of underpants if they want to.