I think it depends on what's observable by the recruiter. If productivity is highly observable, say, from good or bad letters of rec or experience, then you would see certificates negatively correlate with ability but they would have very little informational content. And you would be able to mistakenly have a certificate without it hurting you, since they can see your true ability.
If productivity is not observable, then yes, adding a certificate would hurt you, but it's hard to imagine any separating equilibrium where this pattern is sustained. Everyone should have a certificate or no one should.
That's assuming perfect rationality, though. I would guess people who post certificates don't get how the labor market really functions, while people who don't post them do get it. Knowledge of how the labor market really functions is correlated with ability. So you get a separating equilibrium because a subset of people are ignorant. And I think this is kind of the logic the original article is getting at.
An average business certainly won't have the same recruiting pipeline as Google, to say the least.
Is it the listing of certifications that is inversely correlated with the career progress of the employee? Or is it because listing a certification is strongly correlated to having one, with this being what is truly inversely correlated with career progress? And, if so, in what direction is the cause-effect?
Maybe the tendency to list certifications is correlated to certain personality or attitude that is less likely to progress. Or maybe it is accumulating certifications that is correlated to this. In that case, by not listing them, the candidate will succeed in hiding this fact from potential employers, which may help him or her.
However, what if it is not progressing in one's career that makes one more likely to list (or accumulate) certifications in an effort to compensate? And in that case, all else being equal, maybe the would-be certification-lister would be even worse off were they not to list it!
For a silly analogy, I'm betting that, among users of dating apps, total time spent on them is inversely proportional to the probability of being in a long-term relationship at some point in a given timeframe. However, that does not necessarily mean that using them for long has any causal effect on reducing one's chances.