To deny p, reject p or disbelieve p is most commonly understood in the literature as “to affirm negation”, however to “deny” can mean merely not to accept. However Frege and Geach seem to argue for denying to mean assert negation as “orthodoxical”.
“There is also an operation on contents themselves, taking one content to another, that has long been thought to be importantly related to denial and rejection: negation. For example, both Frege (1960) and Geach (1965) famously argue that denial and rejection should be understood in terms of negation, along with assertion and belief. For them, to deny a content just is to assert its negation, and to reject a content just is to believe its negation. If there is an orthodox position in philosophy today about the relation between denial, rejection, and negation, this is it.”
Which is exactly in line with the epistemic status of “suspending judgment” which is logically ~Bp ^ ~B~p.
Matt seems to be conflating “unbelief” and “disbelief which are two different terms:
Disbelief is more commonly used to express an active mental opposition which does not imply a blameworthy disregard of evidence. Unbelief may be a simple failure to believe from lack of evidence or knowledge; but its theological use has given it also the force of wilful opposition to the truth. [Century Dictionary, 1897]
“Disbelief is a case of belief; to believe a sentence false is to believe the negation of the sentence true. We disbelieve that there are ghosts; we believe that there are none. Nonbelief is the state of suspended judgment: neither believing the sentence true nor believing it false.” -Burgess-Jackson, K. (2017). Rethinking the presumption of atheism. International Journal for Philosophy of Religion, 84(1), 93–111.doi:10.1007/s11153-017-9637-y
This is the issue with using a more privated language as it leads to confusion and inability to properly read much of the literature in context…and to telling callers that they are wrong, when they are not.