Two things:
1. I cannot open the link to Rolls Royce's blurb on how they get their data packets, and how much info each contains. They may be limited to engine parameters only, and just get added to a file for each powerplant, attracting no attention until someone goes looking for them.
2. Regarding the theory of stealing the aircraft: if it was the captain, there is nothing to say he was limited to seven hours of fuel. With sinister intent he could have taken several hours more.
3. OK, three things: It is still possible that the acars was disabled subsequent to the fourth hour if it occurred to the pilot.
4... While this aircraft did not have the satcom antenna that was the subject of the AD it still may have had one, allowing the ACARS to make its scheduled engine health update.