What would cause a broadcast AM or FM radio to receive an amateur radio transmission unintentionally?

The scenario of a broadcast AM or FM radio inadvertently receiving amateur radio transmissions can occur when the receiver lacks sufficient selectivity to filter out strong signals that are outside its intended frequency band. This means that if a nearby amateur radio station is transmitting at a frequency near or within the range that the radio is tuned to, and if the radio's design does not effectively reject such signals, the amateur transmission can interfere with normal reception, leading to unintentional reception of those transmissions.

In contrast, the other options focus on transmitter-related issues, such as microphone gain, audio amplifier overload, and FM deviation settings, which primarily affect the quality and strength of the transmitted signal rather than the ability of a receiver to filter out unwanted signals. Thus, they do not address the core issue of the receiver's capability to discriminate between different signals.