When running the 32bit program on a 64bit CPU the additional registers are simply not used at all. There is no way this can lead to even single byte of extra memory consumption. CPU registers have nothing to with the memory usage of the program. Hence why I said "that's nonsense". You can add 100 more registers to the CPU the memory consumption won't change.
what i should have said is 32 bit programs running in 64 bit can OFTEN use UP TO double the amount of ram usage, due to 64 bit being double the amount of registers