Why doesn't HP LaserJet M1522nf distinguish between received phone calls and faxes?

The HP documentation clearly says that an HP LaserJet M1522nf printer/fax can discriminate between incoming phone calls and faxes.  The phone calls are directed to an extension phone connected to the LaserJet and the faxes are printed on the LaserJet.

I can't make it work.  I've tried all combinations of "Answer Mode": "Automatic", "TAM" and "FAX/TEL" and "Extension Phone": "On" and "Off".  When "Answer Mode" = "Automatic", both phone calls and faxes are identified as faxes.  When "Answer Mode" = "FAX/TEL", both are identified as phone calls.

The faxes received were sent from another, identical, HP LaserJet M1522nf.

This feels like a situation where there is some simple setting that would solve the problem.  Any suggestions?