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The reciprocity theorem is a maths principle but there are differences in transmitters and receivers
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I am prepared to be shot down by this, anyway.
Antennas are reciprocal, I wouldn't expect a ferrite rod to be a good transmitter because it only (well nearly) uses the H (magnetic) field and used as a transmitting aerial will give the same amount of H field but very little E (the electrostatic one). You can easily receive either from the electromagnetic wave, or even both with, say a dipole. You need both H and E to transmit past the near field (a few wavelengths).
Small transmitting loops do work a bit and are used primarily in the shortwave (SW) region (3 to 30MHz) the vagaries of SW mean that upon occasion even a few mW of radiated power can get you "round the world", no one remembers the "contact" that didn't work. Hence the reports of good results from such loops.
Note, not a single SW broadcaster uses a loop, some tried the "crossed field" antenna, they worked due to the co-ax radiating.