I'm not sure that they would disagree. Most people know that a manager can only do so much, if other teams are buying players that are a huge level above, the best manager in the world won't consistently beat those teams.
For me there are two types of manager that stand out from the crowd. One that builds squads, helps identifies young talent and integrates them into the team, and another that can identify short term solutions and use this to his advantage. Both methods involve significant investment and support to make them successful, and without that, the managers can not be succesful, expect with a high "luck" factor, which I think is what you are trying to say.
But for me(and I think for you too) the manager DOES make a difference, just not as much difference as some people like to think. The difference is probably a couple of percent, as this article is saying, but that percent can be the difference between winning a trophy and not. The percent difference a manager makes is probably less than the percentage difference "luck" makes. But I don't think it's been proven how much this percent is, so to unequivocally say it's meaningless, at this stage in our knowledge, is wrong. But then again, I haven't read the research that you might have done.
I think it's correct that some of the statistics we look at are not the correct ones, but I'm still waiting to see which ones are the correct ones. Some possibilities are, shot conversion rates for strikers, chance creation(but how to define this, and differentiate between genuine goal chances and outside chances, is the problem), regaining the ball and keeping it for more than X seconds, time running at full speed, interceptions made(I think this should have distance run correlated in some way, as in the distance run to make an interception should be low, indicating positioning is good). And I'm sure there's more too.
The point of Farks post was for you to share some of the statistics that you've learned are more important, some of the ones I've mentioned probably aren't as effective as I think at present, but I'd(we'd all) like to hear which ones you do think are better.