I read this letter and apart from the patent stupidity of "don't call Mayday on the radio", the 'facts' as stated did not make sense to me in that the "Controller" (as referred to twice) allegedly said "we are XXX TRAFFIC when you call". As far as I am aware TRAFFIC is used e.g. out-of-hours at a FIS aerodrome or for a blind call if no response received from an A/G "Radio" station. In neither case would a "Controller" be involved. That made me question the accuracy of the content of the letter as presented.
Sounds to me like the "Controller" might have been an airborne instructor who, rightly or wrongly, thought that his solo student had made a simulated mayday call with the PTT held down by mistake.