Although an understandable misrepresentation, given the financial loses being caused by the theft of telephone receivers, it was actually untrue that standard telephone receivers "won't work on the wireless sets". However, headphones specially made for radio reception, if you could afford them, were significantly more sensitive than stock telephone receivers.
Telephone Engineer, June, 1922, page 37:

Radio  Craze  Brings  Raids  On  Telephones  for  Equipment

    Chicago, Ill.--From all parts of the United States telephone companies are complaining about the forays amateur radio operators are making on public telephones in order to secure equipment they think will be suitable for their outfits. The seclusion of a telephone booth affords a good opportunity for the radio nut to acquire a receiver. The thrifty and unprincipled parties are greatly disappointed with results of sets equipped with ordinary telephone receivers--they won't work on the wireless sets. Telephone men are hoping the daily newspapers will tip off their readers to this fact and cut down the losses of telephone equipment.