I was about to make a comment about, how a double pendelum can swing in an infinite amount of unpredictable ways, none of which will suddenly turn it into a car. But I like your analogy so much better.
And even an infinite number doesn't mean all. There are infinite numbers between 0 and 1, none of them is 2. So the multiverse wouldn't have to include one that contradicts its rules.
I don't really understand why, but this seems to be a common misunderstanding of the multiverse theory.
All it says is that every possible universe exists, so it's not at all required that everything you can think of exists, just everything permitted by physics. Possible is the keyword here, and you can still have an infinity of universes even if you restrict what is possible.
I'm no expert on the subject, but as I understand it there are generally two types of multiverse theory. The one where you have infinite universes all with the same physical laws, but every unique possibility under those laws exists in the multiverse. And the one where every possible variation on the laws of physics exist (generally talking about different coupling constants rather than entirely different laws). It's entirely reasonable that both types are one in the same.
In either case, it wouldn't really be consistent for there to be a universe where the multiverse doesn't exist, unless it is the only universe and there is no multiverse at all.
Different arrangements would do it, or you could think of it very loosely as the "if you made different decisions in each" kind of thing. Events/history is different, essentially.
On your idea of a "random function" yes, pretty much everything at a fundamental level appears to be probabilistic to some level. Quantum theory cannot in most cases predict the exact outcome of an experiment, just the probability of different outcomes.
You can combine the same atoms into different larger elements. It's like that. The same physical laws, but the combinations are infinite (or at least uncountable).
The other concept is that the laws are different, but not true infinite combinations within reach.
Maybe in the sense that the people there haven't thought of the theory itself. But one universe can't affect if a multiverse exists or not, one universe would just be part of a whole
Going on the rule that the multiverse theory is accurate... Then I do believe that makes the end statement impossible.
The multiverse isn't dependent on any single universe. So if multiverse is true, and a universe exists, it wouldn't be possible for the multiverse to not exist as that would be a logic paradox.
Of course, it's from a matter of perspective. Those in that universe might not be aware of capable of recognizing or conceiving the multiverse. But that wouldn't alter it's existence. Kind of like a one way mirror.