If on the other hand the assumptions are not for example the ping came from another source say SQ68 bound for Barcelona, then that line of enquiry ends right there.
IMHO pings are probably TDMA channel sync or frequency sync bursts. This means, that inside of data, there could be probably two low level identifiers.
1. the HW identifier (something like serial number of your phone (IMEI) or MAC address of you computer)
2. artificial identifier of the connection (which could be correlated with connection information stored previously in time of connection handshake)
There would be no data inside of these burst, as these serve only to SATCOM to keep connection to satellite synced and alive,
I would say that forging data connection on TDMA is possible and it is used for example to intercept GSM connections (man in the middle attack), but this process is definitely not trivial.
I would say, that probability, that these pings were mistakenly from another plane or forged to pretend to be from HM370, is really low.