Thanks to Albert, I realized the 1-volt input exceed the linear range of the P6201 probe. I applied 0.500 V and measured close to 0.500 V at the terminated output. It appears the d.c. performance is fine.
Next I fed 0.500 V RMS at 1 kHz to the probe through a 910 K non-inductive resistor and measured the ac voltage before and after the resistor, The voltage at the probe tip measured 0.0446 V RMS.
Correcting for the measured 868 K a.c. input impedance of the Fluke 8840 meter, I calculated the input impedance of the P6201 probe at 1 kHz to be only 44.7 K instead of 100K per the specifications. When the 10X attenuator head (which is basically a 900 K series resistor at 1 kHz) is added, the division ratio becomes 0.0473 instead of 0.100. This represents a loss of 26.5 dB instead of the 20 dB expected. This is about what I was seeing with the spectrum analyzer. It appears the input FET, Q100, might have damaged gate insulation. Have others encountered this condition?
I am still puzzled about the 103-0164-00 adapter. The probe on my Serial No. B082810 probe has an 0.032 diameter tip which is relatively fine compared to standard test probes. As there does not appear to be a removable front section, is it possible that Tektronix redesigned the later probes to have the smaller 0.032-inch tip so they would not require the adapter for probing ICs?