Re your bolded sentence - only if you are in an agreement with WotC. Mongoose cannot license WotC's copyrighted licence text to you. In that case, you are relying on some other express or implicit permission granted by WotC to use their copyrighted licence text for your purposes.This seems analogous to the situation many non-DnD publishers are in. Let's say I wish to publish a sourcebook for the Cepheus Engine. This rule system is based on the Traveller SRD released by Mongoose Publishing under the OGL v1.0a. I am not using any intellectual property of WoTC with the exception of the licence itself. The right to distribute copies of the license is explicitly granted by OGL v1.0a itself. So what is my relationship to WoTC? Mongoose relied upon representations by WoTC that the OGL v1.0a was available for use by any publisher for any game system. The creator of the Cepheus Engine (Jason Kemp) relied upon the ongoing validity of the licence in turn. And I am relying upon the rights v1.0a conveys upon me to use material copyrighted by Jason Kemp. It's a mess. Which I suspect is the point. I believe WotC may be acting in bad faith to muddy the waters as much as possible.
Various posts upthread (including my own 479) have conjectured where such a permission might be found.
Re your underlined sentence - you are treating the OGL as if it's a statute. It's not. If you and Mongoose and Jason Kemp have entered into licensing agreements on the terms set out in the OGL then (subject to general principles that govern the validity of contracts) you have made valid contracts among yourselves. WotC has nothing to do with this, except that you and Mongoose and Jason Kemp have all promised one another to reproduce WotC's licensed text under certain conditions, so you may have trouble upholding your contractual promises if WotC is in fact able to insist that you not do that.
Hence, again, why you may wish to consider where any express or implicit permissions were granted.
But also pay attention to @Steel_Wind's point upthread: this may be purely academic. Is there any reason, at this stage, to think that WotC cares at all about the licensing agreements you, Mongoose and Jason Kemp have made among yourselves?