If you are off-duty, the DOT cannot make you produce proof of where you spent your night. The only reason they might, is if you say that you went to a hotel. Then they may make you show a receipt. If you are sleeping (at home, a friend's or somewhere elase), but not in the truck sleeper, just log it as off-duty time.
This is one reason that a trucking business owner must know the regs, because many times there are law enforcing yayhoos who do not understand them themselves. If you run your own authority, you must own a copy of the regs book each year. It would probably be a good idea for all O/Os to have one. You could have bought a reg book with your money instead of a bunch of hotel rooms.