I don't see that in my DA20-C1 POH. Under 2.12 FLIGHT CREW it says, "Minimum Flight Crew: one pilot," nothing about the right seat. I've flown the a1's, but I don't know why that would be in the book. The only real difference in the pit is a prop control instead of a mixture control. (A1's are auto mixture, variable pitch, C1's are manual mixture fixed pitch.) Now that I think of it some instruments are arranged differently between the two as well.
FN- what do you mean by "fuel lever"? Are you referring to the fuel cut-off? That's on the right side. (Well, sort of. If you were in the right seat it is just off your left knee. I guess it might be challenging to reach the fuel prime from the right seat.
I've never flown either model from the right seat, so I don't know. But I could find nothing in the C1 book about that requirement.