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I disagree, I believe, they're trying to say they provide "non-reputability" (the opposite to non-repudiation) so you can deny messages actually came from you because they could have been "forged".

it's hard to tell though, the statements are a bit of a mess in general.

Hmm, you're right that non-reputability likely means something different than non-repudiation. The problem is I can't find anyone actually using non-reputability in that other meaning.

What I do find is various places using non-reputability erroneously as a synonym for non-repudiation.[1][2][3] So in fact I now think that EncroChat actually made 2 errors: said non-reputability instead of non-repudiation, and also misunderstood non-repudiation as meaning repudiation.

[1] https://books.google.com/books?id=qk_hDwAAQBAJ&pg=PT682&lpg=...

[2] https://books.google.com/books?id=_d7RUNF-2tcC&pg=PR21&lpg=P...

[3] https://books.google.com/books?id=PHBTDwAAQBAJ&pg=PA61&lpg=P...

I've never heard "reputability" used in crypto, but confusingly, it might be the opposite of "repudiability"?

I read it as saying you could deny writing any specific message as it could have been forged after the session ended. Non-reputability.

Perhaps they were going for non-repudiation?