I don't recall saying you can't do it that way, and certainly didn't mean to.
What I was hoping to do was to explain why you CAN do it that way, since the same thing threw me off when I started thinking about it.
I also like excession's example of running it twice for the separate pots, as it clearly illustrates the problem I was trying to address.
I'm still not getting the claim, though, that the two are independent events. They're connected by an "if-then" statement: namely, if you win main pot, you must win side-pot. Clearly not the case if you run it twice. Then you can win main pot and lose side-pot, the one impossibility in point of fact.