But this doesn’t mean there are actually three possible ways the universe could be, etc.
That’s just a trick for visualizing the path integral. All the amplitude flows actually happen, they are not possibilities.
Corroborated by this peer-reviewed article, published two days ago in Physical Review Letters:
Is a System’s Wave Function in One-to-One Correspondence with Its Elements of Reality?
Although quantum mechanics is one of our most successful physical theories, there has been a long-standing debate about the interpretation of the wave function—the central object of the theory. Two prominent views are that (i) it corresponds to an element of reality, i.e., an objective attribute that exists before measurement, and (ii) it is a subjective state of knowledge about some underlying reality.
A recent result [M. F. Pusey, J. Barrett, and T. Rudolph] has placed the subjective interpretation into doubt, showing that it would contradict certain physically plausible assumptions, in particular, that multiple systems can be prepared such that their elements of reality are uncorrelated. Here we show, based only on the assumption that measurement settings can be chosen freely, that a system’s wave function is in one-to-one correspondence with its elements of reality. This also eliminates the possibility that it can be interpreted subjectively.
Corroborated by this peer-reviewed article, published two days ago in Physical Review Letters:
Link: Physical Review Letters 108, 11. April 2012.