In The Fine Manual for DAOPHOT, available as http://www.astro.wisc.edu/sirtf/daophot2.pdf , the PSF question is covered in detail. A quote from page 32 reads:
For all the different analytic first approximations, the first two parameters are always the half-width at half-maximum in x and y. Any other parameters the model may have differ from function to function, but the first two are, as I say, always the half-width at half-maximum in x and y.
Accordingly, the PSF is invariably elliptical.
See, also, the ALGORITHMS section of daophot> help psf where it is explained that if varorder >= 0, the residuals from the fit are stored as a lookup table, meaning that all but pathologically weird shapes can be handled with ease. In particular diffraction spikes from secondary mirror supports cause no difficulty whatsoever.
I freely accept that DAOPHOT isn’t user-friendly by modern standards but it does a superb job.