Amplitude modulation transmission distortion
It's exactly the same as when using a manually tunable AM receiver. If not tuned correctly (i.e. slightly offset by a fraction) there will be a tendency for a type of high frequency emphasis in the audio received and this is the best that an old fashioned envelope detector can do.

Yes you are quite correct, this is the same when coupling magnetically - the upper sideband will be slightly pronounced compared to the lower sideband. Taking this to extremes and removing the lower sideband will give you a single-side-band (SSB) signal with vestigial sideband or full SSB with suppressed carrier. Neither of these can be adequately demodulated by an envelope detector.