I'm thinking if EM could file a claim and shut them up they would?
No, if you file a lawsuit, you just give more publicity to the claim. Just like when Tom Cruise was accused by some guy of being gay, Cruise sued him (against the advice of his lawyers) and won, but a lot of people still think he is gay (he is not).
BTW, here is the denial from EM:
“While we are aware of Valvoline's assertions, ExxonMobil stands behind the quality of Mobil 1 and all of our lubes products,” company spokeswoman Prem Nair told Lube Report. “ExxonMobil has not lost GF-4 licenses for any Mobil 1 products, and our GF-4 licenses for all product lines are valid.”
Now, I don't really know if Mobil 1 has a problem with the wear test or not. But they do seem to have denied that their oils fail to meet specifications.