Aireps, the maps are very informative, but I don't think SATCOM vs. a ground link is the right inference to base your conclusions. It's not that the Inmarsat pings were initiated by ACARS, but rather by the SATCOM system itself. From what has been released so far, we understand that the ACARS function was turned off, but that action did not fully disable the SATCOM - it only prevented ACARS from initiating any messages.
The "pings" under discussion were empty network keepalive messages sent as a matter of routine functioning of the SATCOM transceiver itself. Imagine this conversation:
"Hello? Anyone there? If, hypothetically, I wished to send some data, could you pass it along for me? Oh, I'm not paid up on this account? So sorry to trouble you. I'll ask again later. Perhaps then I can speak to someone whose bills I've paid."
If that is in fact what the authorities are working off of, then it doesn't matter if any ACARS ground stations were nearby or not, as there was never any ACARS data queued up in the outbox after 01:07 Malaysia time.