I can confirm the veracity of the above account. The "crystal radio" is a tuned circuit where the audio signal is supplied by the broadcast transmitter. The signal is usually very weak and the volume low, you must wear sensitive headphones in most cases.
However, in my High School years I lived adjacent to an AM broadcast station in Virginia, and stretched a wire antenna between some poles. The signal from the nearby transmitter was strong enough to drive a loudspeaker from this location using a crystal radio circuit and an impedance-matching audio transformer. In retrospect I was very probably effecting their broadcast range and propagation pattern by sucking that much energy out of the air.
Note that we are still talking about a fraction of one watt - and it's only "free" to the receiver owner, the radio station pays dearly in several ways to transmit the RF signal into the air.

Modern crystal radios use Germanium small-signal diodes (the component marked "1N34A" above), much rarer than the Silicon diodes that took over all larger power applications. Older designs incorporated some natural semiconductor such as a lump of galena ore (i.e. lead sulfide), held in a clamp and touched lightly by a sharpened wire called a "cat's whisker".

Thanks for the voyage in the "Way Back" machine, I was 8 years old in 1959 when I made my first crystal radio and became interested in electronics. This eventually led me to a career in computers.