If a journal wanted to impose such a rule they would most likely state it plainly. But I think that is very unlikely. It isn't the qualifications of the authors of a paper that make it important, but what the paper actually has to offer. Of course, editors like to know that the authors know what they are writing about, but that is the job of the reviewers to determine and normally reviewers will spend more time with the paper than with the credentials of its authors.
In fact, a paper by an independent researcher without an academic credential might be especially "interesting" if the arguments and conclusions are sound. It might even introduce new ideas into a field. When Einstein did his early work he wasn't well respected by the established intelligentsia of the day. That only came later.
And on the other side, a paper by a brilliant and credentialed researcher that seems to spout nonsense can cause quite a stir.
But, I suspect that in this case, there is some flaw in the paper that the editor noticed independent of its authors. Maybe it was just a poor fit for the journal, or even for the editor's current needs.
One further thought. A restriction on who can publish in a journal, such as requiring a doctorate, would, over time, have a pernicious effect, lowering the quality of the journal. It is the restriction itself, actually any sort of restriction, that leads to some high quality papers not being submitted at all and other, lower quality, ones filling any gaps. The effect would be small, but additive over time.