Hi John

SAW, surface acoustic wave, filters are not transmitter pass filters.

As for the need, that is simple: OF COURSE it needs filtering. Simply
observing the manufacturer's requirements reveals that:
In most cases, the output of the transmitter may need a low-pass LC filter to reduce harmonic emissions.
As for matching:
The output of the oscillator is derived directly from the collector of the oscillator transistor. It is, therefore, very sensitive to VSWR.
This, alone, demands filtering to reduce harmonics.

As for SAW filters. It has one, and uses it in the conventional
manner (not as an output filter) for frequency determination in the
oscillator.

73's
Richard Clark, KB7QHC