He said some things that immediately had me going WTF? for starters, the first experiment AM transmission was in 1906, the same year that Lee De Forest invented (or rather modified Edison's diode) the triode. Commercial broadcasting of AM stations took place in the early 1920s. To make matters even more clear, the JFET (the first silicon based semiconductor) was invented and patented in 1925, although it was expensive and difficult to make. So by all means considering AM broadcasting was the norm and there where towers around for such transmissions and with Transistors in existence, a cell (or mobile) phone is not so far fetched to believe. Around the time it was probably more secretive and in its infant experimentations. The only thing I though that would stump that is the need for a microprocessor, but then again, maybe the phone only could transmit at one fixed frequency and receive at another different but fixed frequency, so therefore, no need for a Microprocessor.
So most likely is was one of the first short distance two way walkie-talkie.