It's hard to know for certain, but that doesn't mean we should throw up our hands and say anything goes. We can still say that some things are more likely to be useful than others.
If you can do arithmetic on arbitrarily large integers in constant time, you can sort lists in linear time.
Also, consider this: it would have been trivial to get a so-called "better bound" on FFT if such a "cheat" were what people allowed.