A better phrasing of the Totalitarian Principle, by Murray Gell-Mann, is "Everything not forbidden is compulsory." There is a subtle difference between saying "is compulsory" and "must occur." They're only equivalent if you're thinking along the lines of the many worlds interpretation of quantum mechanics. And even then, the outcomes don't necessarily occur in the same "world" (so to speak).
The Totalitarian Principle comes about when utilizing Richard Feynman's sum over paths (also called, sum over histories) which involves Feynman's path integrals.
Before Feynman (and Wiener and Dirac), wavefunctions were traditionally calculated by modeling the energy potential, V, and then solving the second order, partial, differential equation called Schrödinger equation, of which there is a relativistic version. This can be a real bear if V is complicated.
The sum over paths approach is equivalent, yet in many situations is much more manageable.
One might rephrase the Totalitarian Principle to say, "When calculating the wavefunction using sum over paths, anything that is possible, even remotely possible, must be included as part of the path integral."
One final distinction is that "anything that is possible" is not the same thing as "anything that is imaginable." It's true that anything possible, even if it is extremely unlikely, must be included in the sum over paths, path integral. But there must be at least a remote possibility. And just because one can imagine something, doesn't necessarily mean it's possible.