I suppose we're at an impasse then, because the claim wasn't mine; nor is it even sufficiently formalized as to be falsifiable (which really was my point here). We cannot apply scientific methods to claims that are only semantically meaningful. For example, the definition of "coin flip" was never even specified, which is why the constant use of the analogy is absurd.
When firms like RenTec exist and continue to empirically generate market-beating returns over 20-30 year timespans, the burden ceases to be on the critic of a claim to empirically disprove it, especially if it's not even falsifiable. Here, you are doing the same thing as the previous commenter, except you're not using the analogy.
You cannot open your argument with the premise that returns are purely stochastic if that's not self-evident - you need to prove that. But I have never seen a single individual attempt to quantify the analogy, not even in a forced way to make it support their thesis. It's taken for granted that superlative returns are purely chance, and the goalposts are constantly moved whenever someone brings up successful funds.