I think the key point that makes the quoted statement sciencey gibberish is that the Many Worlds Interpretation is just that - an interpretation. There is no way to prove or disprove it (except if you proved that the world is not actually quantum mechanical, in which case MWI might not be a valid interpretation of the new theory). Saying "this is more evidence for MWI" is thus true of any quantum mechanical experiment, but anything that is evidence for MWI is also exactly as much evidence for Pilot Waves (well, assuming it is possible to reconcile with quantum field theory), the Copenhagen Interpretation, QBism, and so on.

As a side note, there is still a huge gap between the largest system we've ever observed in a superposition and the smallest system we've ever observed to behave only classically. So there is still a lot of room for objective collapse theories, even though that space has shrunk by some orders of magnitude since it was first proposed. Of course, objective collapse has other, much bigger, problems, such as being incompatible with Bell's inequalities.

Edit: I'd also note some things about MWI. First, there are many versions of it, some historical, some current. Some versions, at least older ones, absolutely did involve explicit branching. And the ones that don't have a big problem still with explaining why, out of the many ways to choose the basis vectors for a measurement, we always end up with the same classical measurables in every experiment we perform on the world at large. Especially given that we know we can measure quantum systems in another other basis if we want to. It also ultimately doesn't answer the question of why we need the Born rule at all, it still postulates that an observer only has access to one possible value of the wave function and not to all at once. And of course, the problem of defining probabilities in a world where everything happens with probability 1 is another philosophically thorny issue, especially when you need the probabilities to match the amplitude of the wave function.

So the MWI is nice, and it did spawn a very useful and measurable observation, decoherence. But it's far from a single, satisfying, complete, self-consistent account of the world.