Knowing no more than what you've said, I agree with @NickCox, @AdamO, and with you for the most part. If you have discussed this "completely mischaracterized" work in further depth than you've said here, it may not be safe to assume the objection is mostly to your characterization of it as "correlational", unless the reviewer has made that really clear. His/her objections seem very emphatic, so you're right to suspect s/he is an author. Might you be able to talk to this reviewer more directly to seek consensus (or at least compromise) on how to describe the work? I suppose some review processes might rule out conferral outside the formal framework, but it seems counterproductive in this case if you can't work together with this person.
Of course, this isn't to say there's any certainty of whom you're dealing with beyond what you actually know; I only agree it seems likely, and echo the other Nick's suggestion to seek clarification from this person. It would seem to be in your mutual best interest to describe everything optimally from both perspectives. Hopefully all the initial bluster will die down as you communicate further. Sometimes people begin by making a bigger fuss than is really necessary just to ensure they get your attention and make an impression, despite the evident risk of that being a worse impression (e.g., biased, unreasonable, alarmist). It's easier for some to proceed with restraint and mutual respect once they've been reassured that the lines of communication are open and the other party is paying attention. It seems you've made the opposite first impression with what you've written, so an overblown reaction is understandable, if still unreasonable. Clarification should help greatly if s/he's willing to work with you.
Regression is indeed correlational in the broad sense, as has already been said here, but the strictest, most simplistic sense of correlational may appeal to those who have a less nuanced understanding of general linear models. The stricter usage may also appeal more to people who understand correlational analysis as a loaded term in causal research contexts, such as your problem reviewer, it seems. If your intention was to imply a weakness in causal evidence, then your usage was loaded intentionally, and some defensiveness is to be expected. You'd be right to say that multiple regression doesn't really provide more causal evidence than a bivariate correlation (the stricter sense of "correlational" that AdamO described) – it mostly makes relational evidence clearer regardless of whether these relationships are causal. Hence I doubt your reviewer is simply objecting to your characterization because the method involved multiple regression, not just bivariate correlations. Maybe the reviewer felt the original design had other, "more sophisticated" elements that provide "much stronger evidence". Maybe I give this person too much credit though; I've been led to think one should never underestimate the capacity of reviewers to overreact to issues that amount to nitpicking.
Generally, I wouldn't object to describing regression as correlational, and might have done so myself in your case initially, but given the apparent offense this has caused, I don't see any harm in backing off and rephrasing. If your intention was to imply critique of causal evidence, it would be better to state the critique clearly and delicately, not to just imply it. If your alternate phrasing of the "distinction between statistical and mechanistic relationships" captures your meaning just as well, maybe you can avoid the issue by replacing the "correlational" phrasing entirely, but again, if you can confer with your reviewer about this alternative, you'll stand a better chance of having the change received well, of course. AdamO has provided some other good alternatives, and your comment on his answer seems quite a bit clearer about the distinction you intended to make between your work and your reference. As for "empirical", I think you're encountering the same basic issue by using a single word with a variety of possible interpretations where several sentences that clarify your intention with context would be preferable.