They did deliver. They deleted everything on their servers related to that customer that they claim to. It seems unrealistic to expect them to purge third party services as well.
The wording on the $19 service [1] is very clear to the extent of the services they are providing, specifically:
* Removal of profile from search results
* Removal of profile from site
* Removal of messages sent and received
* Removal of messages from recipients mailbox including winks and gifts
* Removal of site usage history and personally identifiable information from the site
* Removal of photos
While the second to last bullet is a bit ambiguous and you could make an argument that billing information is personally identifiable, this specific indication of "from the site" implies (to me at least) that it is referring to Ashley Madison servers and not third party credit card processors.
