What does the standard claim that detecting a closed universe would rule out the multiverse mean?

Question

The new article "Lorentzian Vacuum Transitions: Open or Closed Universes?" On page 41 reads:
"We believe that the possibility that the geometry of the bubble after nucleation corresponds to a closed FLRW universe, contrary to CDL, should be seriously considered. Indeed this is the natural implication of brane nucleation in string theory as we have argued in this paper. This may have important physical implications if our universe is described in terms of a bubble after vacuum transitions as discussed at the end of the previous section Besides the deep implications of having a finite against an infinite universe, with finite number of stars and galaxies, it may eventually be tested if there is a definite way of determining the curvature of the universe. For the string theory landscape, it will at least eliminate the standard claim that detecting a closed universe would rule out the multiverse. These are important cosmological questions that deserve further scrutiny ".
What does the standard claim that detecting a closed universe would rule out the multiverse mean? If cosmologists find that the universe is closed and finite, would that rule out the existence of the multiverse and other universes?
Article link: https://arxiv.org/abs/2011.13936

Eletie · Accepted Answer

I've not read the full paper you listed there (and it definitely doesn't look like a quick read), but the following passage by Ellis seems most relevant:

The multiverse idea is testable, because it can
be disproved if we determine there are closed
spatial sections in the universe (for example, if
the curvature is positive).

The claim [above] is that only negatively curved FRW
models can exist in a multiverse based on chaotic inflation, either because Coleman–de Luccia tunnelling only gives negative curvature
or because a closed spatial section necessarily
implies a single universe. But the first argument
is disputed (there are already papers suggesting
that tunnelling to positively curved universes is
possible) and the second argument would not
apply if we lived in a high-density lump imbedded in a low-density universe (i.e. the extrapolation of positive curvature to very large scales
may not be valid)

taken from the article Universe or Multiverse, (bullet point 3), the whole of which may be worthwhile reading. As said in the quote, he's referring to a multiverse in the context of chaotic inflation, but within the article he makes reference to the string landscape, though I don't think I'll do it justice by picking out any more quotes.
From what I gather, the quote from your paper is saying that, the claim: a closed universe is inconsistent with a multiverse scenario, is no longer correct. Ellis also seems to be saying the same thing, except making the point that this implies the multiverse is not testable. Different arguments based on the same core idea. The reason why the claim does not apparently hold anymore is listed in my long quote from Ellis above (and references can be found therein that are more technical).
Related article: https://academic.oup.com/astrogeo/article-pdf/49/2/2.33/683010/49-2-2.33.pdf

What does the standard claim that detecting a closed universe would rule out the multiverse mean?

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