The fact that they've already deleted all user address book data, and have an updated version of the app available today with a privacy option, is a big deal. I don't know how they managed to get an update to the app approved so quickly (24-48 hours?), they must have worked directly with Apple. A good sign, either way.
IIRC, Path's CEO commented on the post that initially reported this behaviour saying that an update had been submitted that would make it an optional feature prior to the report.
Any dev can appeal to Apple to expedite a review when there is a good reason. I've done it several times and they generally have it reviewed within a few hours and out within 24. It's good that they've done this though and deleted all the data.
You can't prove a negative. You can only prove the existence of certain data on a particular server, you can not prove that a company does not have certain data unless you are prepared - and they are willing - to give you full access to audit each and every byte on their systems and to wipe any parts that they can't explain and you can't find a way to decrypt.
Clearly that is not practical so we'll have to take them at their word, as it stands I think that if path is found out to be lying about this that it will come back to haunt them big time.
It probably would help if they had an outside auditor to verify the actions that were taken. Still wouldn't be final proof to anyone who believes that they might still be hiding something but is a step further than just saying "trust us".
Better than ATT, VZW, MS, TW, Comcast, or any national US bank.