most of a DSLR's weight is lens and battery(s), both of which are not issues in this case, since the lens would be the same and the power comes from a nuclear battery.
NASA couldn't just bolt on a 5DmkIII and expect it to work because the electronics would be fried.
That said, the Apollo missions took a not-very-modified Hasselblad camera with them that worked fine, which is why we have much higher resolution pictures of the moon, despite it being decades ago.