On the other hand, the FM signal is radiated from an antenna atop the
tower. Stand at the base of a 300' FM tower, and you're 300' from the
thing that radiates.

This is the same theory in which people claim using their cell phones are safe,
because the power they put out is so low.

They are powerful enough to transmit to cell towers miles away! Now put that
power inches from your head and how more concentrated is that power?