That line from Wikipedia gives two citations, the latter of which is to
Hand, D. J.; Yu, K. (2001). "Idiot's Bayes — not so stupid after all?". International Statistical Review. 69 (3): 385–399. doi:10.2307/1403452. ISSN 0306-7734.
An excerpt from the end of their section 1:
Before commencing, however, some clarification of the word 'Bayes' in this context is appropriate. In work on supervised classification methods it has become standard to refer to the $P(i)$ as the class $i$ prior probability, because this gives the probability that an object will belong to class $i$ prior to observing any information about the object. Combining the prior with $P(\mathbf x \mid i)$, as shown above, gives the posterior probability, after having observed $\mathbf x$. This combination is effected via Bayes theorem, and it is because of this that 'Bayes' is used in the name of these methods. [...] The important point for us is that no notion of subjective probability is introduced: the methods are not [necessarily] 'Bayesian' in the formal statistical sense. [...] In this paper, following almost all the work on the idiot's Bayes method, we adopt a frequentist interpretation.
The Wikipedia claim, I think, is just that naive Bayes need not be interpreted as a Bayesian method based on a subjective prior and so on; it makes perfect sense to think of it as a frequentist method. Similarly, note that the Bayes classifier is not an inherently Bayesian concept, but in fact comes up in frequentist analyses quite often; the naive Bayes classifier is simply the Bayes classifier under a certain independence assumption, and so that need not be a Bayesian method either.