I think you are wrong here.
The only assumption being made is that the ones for whom party affiliation could be determined from NYS registration information were politically representative of the whole. This probably isn't an off-the-wall assumption as it is unlikely that a potential faculty member is asked about his registration during the hiring process.
After that it's just simple statistics. I don't feel like figuring it out now, but if half of the faculty was sampled the margin of error in estimating the division of the entire faculty is quite small.
ML/NJ
The unknown variable is the total number of faculty at the college. If there are 1000 faculty members, then knowing the political affiliation of 120 would not be sufficient to predict the political affiliations of the remaining 880, particulalry since the 120 faculty members were not chosen at random. But if 150 is the total number of faculty, then the analysis of the political affiliations of the known faculty is sufficent to predict the affiliations of the unknown. Either way, I have no doubt whatsoever that the vast majority of college faculty throughout the Country are well left of left.