That statement is just mystical dogma unless you can explain why they are the same thing.

I won't say the truth of the mathematical universe hypothesis is self-evident or anything, but there's certainly nothing mystical about it. All it says is that there was never any reason in the first place to suppose there's a difference between possibility and existence. It's not like we have perfectly clear concepts of 'possibility' and 'existence' that clearly conflict with one another.

The best analogy I can think of is the statement that time is the same thing as a coherent set of universe-configurations. Why are they the same thing? Um, because that's what time is. What makes you think it's anything else? Likewise for existence: What makes you think it's anything other than possibility?