I remembered having read about Maekawa's theorem about flat foldability on an inner vertex being disproved but I could not remember where but finally I found what thread it was, it is this one: viewtopic.php?f=16&t=12181&p=132045

Specifically:

Razzmatazz wrote:Determining if it is flat fold-able via Maekawa's and Kawasaki's theorem has been disproven. However it is a good general rule.

And latter Razzmatazz was asked to provide evidence:

PauliusOrigami wrote:

Razzmatazz wrote:Determining if it is flat fold-able via Maekawa's and Kawasaki's theorem has been disproven. However it is a good general rule.

Could you give me a reference (source)?

But Razzmatazz's answer is based on an article that to be read needs to be purchased first:

I remember finding a presentation online (unfortunately, I can’t remember where) that touched on the (dis)proof of the theorems, giving crease patterns of a couple counterexamples. I have it saved on my computer, however; so maybe I can send it to you. (This assumes that I’m thinking of the right one.)
As far as I can remember, it has something to do with the law of origami that a sheet can’t intersect itself. In essence, two vertices that would ordinarily fold flat on their own may not fold flat together if they’re too close on the paper.