I thought about this for a while and came up with a tight argument:

First, note that it is implausible to claim that academic philosophers are the only people doing philosophy. There are certainly private individuals engaged in the search for philosophical truth as well - Nassim Nicholas Taleb and Eliezer Yudkowsky are two such individuals whose names spring immediately to mind; there are doubtless many others. To claim that only philosophy professors can do good philosophy would be like claiming that only literature professors can write good literature.

Given that there are many non-academic philosophers out there, if we assume that academic philosophers (and philosophy journal editors) are disinterested truth-seekers who are not motivated by political and status concerns, then we should expect to see articles written by non-academics published frequently in philosophy journals, or at the very least we should expect academic philosophers to frequently cite the non-academics.

So, not knowing the actual state of things, since I don't read many philosophy journals, I will expose my theory (academy philosophy is not about truth-seeking) to falsification by predicting that philosophy journals almost never publish articles by non-academics (i.e. someone without a university affiliation and a Phd), and academic philosophers very rarely cite work done by non-academics.