The issue of contemporaneous notes has a long legal history. On the positive side, they carry orders of magnitude more weight in court than anything you wrote down later. On the negative side, they can be subpoena'ed. This has been true since long before any kind of digital record-keeping. Creating false "contemporaneous" notes is a big deal. Do not do it.

To answer your question, yes, that's probably enough, but a hard-copy log-book is always the best. Even just notes in the owners manual counts. The key, as suggested above, is that you write it down when it happens.

 

Screw that. Get a lawyer and watch them pucker up really quick. They are trying to bend you over royally.

 

Great your fiance has the receipts! If they give you any more trouble then I would lawyer up.