We are happy to report that
https://bitbargain.co.uk (a fiat<->btc marketplace) told us that they successfully used TLSNotary in an unusual case where bank lost the buyer's payment.
Even though
https://bitbargain.co.uk processes ~300 trades per day, twice a year they'll have a situation where there is no way to resolve a disagreement between reputable parties.
Using TLSNotary the seller showed to the BitBargain staff their online bank's statement page (with a cryptographic proof) without revealing their bank's login/password. Good times.