I think that may be a misunderstanding brought on by differences in languages.I found it to be a flaw in Tyrians claim, that he was looking for the truth, since a trained historian would never claim that the truth existed as some sort of information that did not need interpretation either by the one who originally created this information or the one who discovered it. Therefore there can never be a "numerical truth"
Nobody in their right mind would claim the Tsunami of 2004 killed a lot of people and that the order of magnitude is what it has been reported to be, right ? Now, in 60 years I do not see it unlikely people could start guestioning the number of dead at being hundreds of thousands, only because there is archival evidence of only the tourists who were killed in the disaster. Hence people could claim only a couple of thousand "people" were killed and not the enormous amount the period news media "would have us believe".
Another example is the numer of Red Army KIA during Winter War. Molotov claimed under 50 000, Chrustsev over a million casualties. Contemporary Russian research has put the number at around 130 000 KIA. The Finnish estimate has been 200 000 since 1940.
This is why I think there can be absolute (or very close to being that) truths when it comes to numbers and other quantifiable and verifiable data. And this is why there is some merit in Tyrians angle of approach.