You are both partly correct.
In analogue free space transmission, it is possible to have too strong a signal, and for distortion to occur. Radios have ways of managing this, however. Receivers can control the attenuation and gain of the received signal, to maintain signal level within an acceptable range. Weak signals will still have a degraded signal to noise ratio.
The physical layer of a digital receiver is still subject to similar issues, though distortion is usually less of a factor. A simple digital receiver, with no signal conditioning, and no filtration, will severely suffer from the kind of distortion you are talking about. Of course, it's not done that way in practice.
If enough radiated power were received, then distortion can still occur. This can be seen quite clearly with a 1kW transmitter adjacent to an average receiver of the same frequency.
Using a speaker to convert electrical waves to sound waves is not the only possible source of distortion in an audio system. All devices have nonlinearities, and generally when overdriven, will introduce distortion.
Hope that's clear enough, without going into details.
