Contra proferentem is most important with "contracts of adhesion" like OSS licences that are pre-written contracts which are strict take-it or leave-it, leaving no opportunity for a party to bargain over specific contractual terms. Because the party does not have an opportunity to negotiate they may reasonably interpret a term in a different manner than the contract offeror intended.
The court would likely rule that the more comprehensive document takes precedence (exactly what the AGPLv3 intended.) Less likely outcome is that the court decides there was no valid license at all. This would technically be copyright infringement, but they almost certainly wouldn't issue sanctions because of the innocent infringer principle. Sneaky Company, Inc. messed the license writing and that makes copyright infringement understandable.