Three different times my Hampton bay remote fan came on by itself in the middle of the night on high. No one lives near us that would have the same code.

We've been having the same problem for a long time... I would very much be interested in knowing how to resolve this issue.

Try different dip switch settings. See:

Ceiling fan remote controls - help and FAQ- Ceiling Fans N More (http://www.ceiling-fans-n-more.com/ceiling-fan-remote-controls.php)