As someone who can count "Senior Scientist" among his formal job titles I feel motivated, if not obligated, to comment ...
Agreed, but ... It also depends on who's being asked, as I hope to explain below ...
Academics tend to accept only those fellow members of the club, those with the requisite post-nominal scrabble, a few published papers and the links with industry that tend to be developed as a result.
The media tend to follow the academics' lead, but they're more likely to adorn the title 'scientist' with approving or disapproving adjectives; in the latter case, they're often disqualifyingly negative, which in turn paints a picture of a 'true scientist' as some kind of cloistered ascetic, likely possessing no political beliefs beyond those required to facilitate open enquiry and the exchange of ideas, certainly not giving public voice to their personal views regularly. ...
Here's the terminological and conceptual issue that most people don't recognize at all ...
Nobody is awarded the title "scientist" as the reward for completing an academic process. There are no diplomas that certify the designee as a "scientist." The recently-departed Freeman Dyson is an example of an eminent "scientist" who never completed a PhD.
To be sure, academics evaluate, associate with, and self-identify themselves as peers / equivalents based on credentials, publications, accomplishments, affiliations, etc. - just as any other set of individuals will do using whatever criteria their set's social context prioritizes. These interactions and affiliations can be just as self-consciously "club-ish" as any other self-circumscribed social group.
To the extent there exists such a club (or set of local clubs), the self-identification has to do with the accoutrements of academia rather than any particular disciplinary sector within academia's vast disciplinary range. You'll find the same club atmosphere among academics in (e.g.) the arts and humanities.
If "scientist" isn't somehow naturally or automatically derived from one's academic background, what is it? It's almost always a general / casual label attributed by someone external to any "science" or "research" per se - e.g., journalists referring to a subject matter expert / researcher or managers assigning labels to the eggheads on their organization charts.
At best, this external labeling is done by more or less approximating the dictionary definition - i.e., a person studying, knowledgeable in, or conducting research regarding a "science", especially one of the natural or physical sciences.
This in turn runs into the ambiguity regarding what counts as a "science," I've personally known "hard science" professionals who discount anyone working outside the scope of the classic physical sciences and a strict by-the-book scientific method (a la Sheldon Cooper in
The Big Bang Theory). To such doctrinaire strict interpretationalists Peterson doesn't qualify as a "scientist" in the first place. Even using a looser interpretation, Peterson's background in a "soft science" (e.g., the social or applied "sciences") means one's answer will depend on where he / she draws the boundary line.
This same conundrum recursively applies within psychology itself. I know (e.g.) experimental and behavioral psychologists who'd consider clinical psychology a matter of philosophical or speculative inquiry rather than their own "scientific" subset of the field. Peterson is vulnerable to this opinion based on his grounding so much of his work in Jung - who, like Freud, can be construed as a perceptive and persuasive speculative thinker whose theories aren't subject to reasonably objective testing, much less falsification.
Going even further ... Much of Peterson's work can be just as easily classified as "philosophy" rather than "science." This doesn't clarify anything, insofar as the same issues mentioned above can be found among the community of academic philosophers, and third parties (e.g., journalists) are all too willing to casually categorize someone as a "philosopher" in the same way they casually label someone a "scientist."
Similarly, we have all seen a number of 'fringe scientists' in the field of Forteana who clearly pursue some form of scientific method, but who lack the requisite qualifications (academic, professional and social) to be granted the title 'scientist'. ...
Given what I've expressed above, I'd say such fringe thinkers / researchers are attributed the "fringe" attribution on the basis of the external / third-party basis I mentioned above as much as by any snooty condescension from the academics' club(s). I'd also point out that some such "fringe" researchers would still qualify as "scientists" if the label were based on academic credentials alone - further demonstrating the futility in linking the label to academic background or affiliation.