Nonsense. You should be more careful with the word "never".
The FCC requires a limiter before an FM transmitter to avoid overmodulation.
With an FM transmitter, over-driving the transmitter will produce illegal frequency deviation, but have no effect on the power stage.
Limiting the input to an FM transmitter is very important, since modern US FM transmissions include the multiplexed-stereo signal and an "HD" or hybrid-digital subchannel as well as the baseband, and the peak levels of the total waveform are what cause overmodulation.
With an AM transmitter, over-driving may cause the output stage problems on the positive peaks, and the negative peaks will give substantial distortion due to clipping.
Whatever can go wrong, will go wrong, and over-driving something is rarely a good idea.
(In my experience with AM broadcasting, we kept a simple CRO on the RF output to see the "dashes" caused by negative overmodulation.)
Since overmodulation is possible, yet bad, radio stations employ peak limiters to avoid it. They may also compress the signal to reduce the dynamic range to cope with SNR problems.