Regarding the pKa values, I agree. i do not agree with the mechanism. Perhaps that will help. If you add HCl to water or methanol, a lot of heat is evolved. Presumably this is due to protonation of the oxygen and forming the ions. Therefore, as suggested, methoxonium ion is the acid and methanol is the base. Chloride is simply a bystander ion. Of the ions present, a small amount of the time, the carbonyl group becomes protonated (or perhaps only collides with a proton). Once this happens, the protonated carbonyl is more electrophilic and can accept electrons from another oxygen.
One might also reason that electrons from the ring oxygen might also collide with the carbonyl group. That would increase the basicity of the carbonyl group. An intramolecular collision would be more favored by entropy than an intermolecular collision. Remember, an uncatalyzed reaction can also occur with water on simple aldehydes to give a hydrate, formaldehyde is completely hydrated (as I recall).