This is a matter of style, so I doubt there's a concrete rule.
You could certainly use the APA Style & Grammar guide to support your point, specifically Section 4.11. However, this is more nuanced than apparent at first sight.
I will first state the relevant text/links, followed by some caveats and nuances which may be worth considering.
Quoting from this useful page (emphasis mine):
Anthropomorphism is the attribution of human characteristics to
nonhuman entities, objects, or concepts. It results in ambiguity or
misleading communication and thus should be avoided in APA style.
However, common usage in academic writing includes some phrases such
as "the results suggest" that, although examples of anthropomorphism,
are acceptable for use because they do not lead to confusion.
And from here:
Correct usage: The theory addresses
Incorrect usage: The theory concludes
Rationale usage: A theory might address, indicate, or present, but researchers (not theories) conclude.
Now, the caveats. @Schmuddi has correctly pointed out that some examples on the first link directly address your specific point. These examples, all of which are considered applicable are :
This section addresses
This paper focuses on
The results suggest
The study found
The data provide evidence that
Thus, the specific example seems above board based on general perception as well as the APA guide.
A broader question is whether the APA guide is infallible; @DanRomik and @Wrzlprmft have correctly observed that the APA judgment on what constitutes anthropomorphism is somewhat arbitrary, and some examples contain a logical fallacy, such as :
The theory concludes
The fallacy is that a theory cannot logically conclude anything, so anthropomorphism is moot. A section, manuscript, article, or comment can. In these cases, one must decide if the usage is appropriate. (Of course conclude has two meanings, deduce and end, and we are talking about the former. It is possible for a theory to conclude a lecture.)
This brings us back to the beginning; this is a matter of style, so in ambiguous cases, one must apply one's own judgment. APA recommends rewriting when in doubt:
If you are unsure whether a construction constitutes anthropomorphism,
try rewording the sentence or choosing a different verb.
My personal suggestion would be to do so if the rewritten sentence doesn't become clumsy, wordy, or otherwise unnatural. As a teacher, probably it is best to make students aware of these conventions and leave the choice to them.