As Cougar has already pointed out, there are many more 'options' than just the two you cite.
For example, the filters used to measure magnitude, at any given time, are fixed according to the zero redshift Earth, rather than the quite different redshifts of all the objects. Although Hawkins mentions that several bands were used, and provides a reference to a paper where the data reduction and error analysis are to be found (I've not read that paper), I rather doubt he could easily control for any such effect.
Another example is
evolution; in the mainstream view, quasars changed quite a lot as the universe aged. Hawkins implicitly assumed that the intrinsic quasar variability is independent of the quasars' ages.
Finally, Hawkins did not - as far as I can see - attempt to what classes of variability models could be ruled out to what degree by his study.First, I'd like to re-iterate that, in science, one cannot 'prove' or 'disprove' anything. As a long-time member to at least UT, I expect that you're familiar with why this is so, and could probably rephrase this in a way that's more in tune with what science is actually about.
Second, there are many, many approaches you could take to address the question of time-dilation in quasar variability, ranging from more of the same sort of data, data from different telescopes/detectors, taken over different periods, to analyses that put more rigourous statistical constraints on the results coming from such analyses, to estimating intrinsic variability from quasar models (i.e. SMBH + accretion disk + torii + jets + ...).