[raattgift]

No, GP means (in the second line) that because nature (and particle colliders) perform so many "experiments", even very rare outcomes will be spotted eventually.

It's a statistical statement about many particles (or field-values in a sufficiently large spacetime(-region)-filling set of quantum fields), not an interpretational statement about a single particle.

[aaachilless]

Then I don't understand this, from the article that was cited:

In the many-worlds interpretation of quantum mechanics, the principle has a more literal meaning: that every possibility at every interaction which is not forbidden by such a conservation law will actually happen (in some branch of the wavefunction).

[raattgift]

The key there is "at every interaction".

Consider lots and lots of interactions.

In what I was explaining, you have highly probable outcomes being observed a lot, and very low probability outcomes being observed rarely.

In what you are reading on wikipedia, you have at each and every one of those lots and lots of interactions a "splitting" into a different world per possible outcome. That's MWI's core content, and it seems to help some people develop intuitions about outcomes of experiments where small numbers of interactions (perhaps even just one, especially where it involves entanglement) determine much larger systems.