Earlier quoted context omitted.
Yes, but it isn't.
It almost certainly is - there is a single phenomenon in physics that has any chance of being non-deterministic (the interaction between a quantum system and a classical system, "measurement") - otherwise all of the rest of quantum mechanics and classical mechanics and general relativity are fully deterministic (though chaotic).
>there is a single phenomenon in physics that has any chance of being non-deterministic
In other words, we've managed to prove pretty much all of physics is built atop this one single phenomenon. You might as well say we've simulated lots of universe models on computers, and yet there is only a single universe model that has any chance of not being simulated on a computer (ie the one we're in), therefore all universes are probably simulated on computers. Sure, its a valid theory, but it begs the question of whether there is a universe at the bottom that isn't on a computer, or is it really an infinite line of computers stretching forever?
Non-determinism is inherently going to be at the bottom of the "layers" of physics, if it exists. If it feeds up to higher layers it will have to feed through each layer of the chain, so inherently we'd expect most layers of physics to deterministic, even if it exists. Therefore our intuition from higher layers isn't helpful in predicting lower layers unless we think those lower layers are built atop even lower layers below them.
Currently the most widely concidered deterministic theory is that there's a deterministic multiverse (ie all events we currently see as random are simply deterministic branches within the tree of all possibilities). But effectively that means the universe isn't actually deterministic, in the same way that if you have 5 boxes with 5 numbers in them, opening a box at random is not deterministic, even though opening all 5 simultaneously without an order _would_ be. The non-determinism is what we end up experiencing, rather than what happens within the multiverse, but it's still there (well, its not from a multiverse perspective, but it is from our perspective unless and until we find a way to see outside our branch of the multiverse).
There's other deterministic theories, but pretty much every theory is untestable, so more a question of faith than science.
Einstein famously agreed with your interpretation, but his invoking of god to make his case is quite appropriate.