12:59 PM PT -- Judge Mathis is clearing the air and setting the record straight on what exactly happened with his alleged spitting incident -- denying any saliva left his mouth, and even dropping another crazy nugget on us ... the actual wait time for his car, way longer than 15 minutes.

Mathis came on "TMZ Live" Wednesday to defend himself against the valet's allegation, flat-out saying he did NOT spit on the guy as he claims. He says he ended up waiting a whopping 40 minutes for his Rolls-Royce to finally be brought around ... 40!!!!

Judge Mathis says he got into a verbal back-and-forth with the guy, but that's all it amounted to. He says there were several witnesses who can back up his story, and he also told us he was not aware of any police report. He says he hasn't been contacted by cops.

To make matters worse, Judge Mathis says there was something very important he needed in his whip, which probably exacerbated the sitch. Watch ... ya kinda feel for him.

Judge Mathis[1] might have to go in front of a judge himself because he allegedly lost it on a valet and spit on him ... and TMZ's learned the guy's lawyered up.

Sources connected to the valet tell TMZ ... the TV judge valet parked his Rolls Friday at Flood's Bar and Grille in Detroit, but when he left the joint ... things got hot quickly.

We're told a valet had Mathis' keys in his pocket and was out on a run to retrieve another car, and was gone 10-15 minutes. Our sources say

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