I have come across some documents (not publicly viewable) that state that footnotes (for the purposes of adding further information) are not permitted in an academic text writen using in-text citations. This seems nonsense to me and I strongly suspect it is a misunderstanding that has solidified into a rule in this particular academic sidestreet.
Could anybody point me toward a reputable source (or at least a definitive example) indicating either way on the issue?
The fallacy here is the idea that there are general rules at all. There are no general rules about what is allowed in an academic paper, or any other kind of writing. There are specific style guides -- some public, some specific to a particular institution or publication -- and their rules cover the particular institution or publication that publishes or ascribes to them.
So, the only requirements that you should worry about are those imposed by the particular publication or institution you are writing for, and those rules should be contained in a particular style guide.
If two style guides differ on some rule, this is not a disagreement, it is merely a difference. If two soldiers from different armies exchanged clothes, then both their respective commanders would consider them to be out of uniform. But if they met a soldier of a different army in the uniform of that army, they would not consider them to be out of uniform, even though the uniform they were wearing was different from their own.
footnotes (for the purposes of adding further information) are not permitted in an academic text writen using in-text citations
That is 100% true according to some specific guidelines, while it's not for others. Citation style is not a universal law. It is a set of conventions used by a community. Therefore rules change from field to field. In my institution for instance the guidelines for authors specify that footnotes must be really short, and not used to write extensive explanations. They are a guide for authors, not a "right or wrong" type of law.
On the other hand, in my literature studies, academic papers all had huge extensive blocks of footnotes, sometimes longer than the text itself.
So, I don't know what style book you are reading from, but what you see as "nonsense" can be perfectly reasonable according to a specific policy.
