You don't argue that mutation is not probabilistic because you know that it is. We have already established that you will use the term 'random' when you understand that probabilistic is the correct term to describe mutation. That is the fallacy of equivocation.
I quoted the only science that was done in that article because that was all that was relevant to the question we were discussing. How the mutations achieved the probabilistic distribution found by the study is where the authors committed the fallacy of affirming the consequent. You argue in favor of the fallacy because it is irrelevant to the argument about whether it is appropriate to use the term 'random' when you should use probabilistic.
It's clear that you are the one who doesn't understand the difference between science and fallacy.
Someone else sequenced the p53 gene in those different species and entered it into a databank.
They looked into the databank and compared the sequences for those eleven species, finding that those responsible for the region that would bind to DNA were less likely to be different between species. This was a “dry” experiment. They only played with the sequences with math.
So how is this supposed to determine the frequency of mutation?
Short answer...it doesn't.