Continuously saying "minimum length could just be smaller" is a god of the gaps argument. Technically correct but wildly suspicious, particularly if your theory doesn't actually say what the minimum length ought to be, eg. it's borderline not falsifiable if you can keep moving the goalposts.

I assume the paper she and Brian Keating are talking about were very explicit in how they tested this property and how Lorentz invariance was expected to be violated, so you could check the paper for specifics.