Clearly theres lots of folk with axes to grind.
If you search out the un-edited audio from LiveATC (19.6 15:00 - 15:30z EIDW) and listen to it you get this:
15:04.23 81D: request push
15:06.31 GND <unintelligible > ...caution BA will be pushing back to charlie
15:06.35 GND: <confused blabber> ... caution ATR pushing behind you (but that seems to be to Ryan 7316 from the following ack)
15:07.53 GND: <unintelligible> ...pushing back behind to you to point bravo
15:08.19 81D: BA makes is call that push has stopped.
There is no proper call from GND warning BA, (at least not one that has an intelligible callsign) Thus it's not surprising that they didnt respond.
And there's only 1 call at 15:07.53 which could have been it. Thats a single call, not 'i have been trying to call you) and only with 15 seconds warning.
IMHO this is a ground control error, and the controller is the one trying to transfer blame. IMHO the 81D pilot is perfectly entitled to be shirty and correct to flag it. The professionalism comes purely from the others on freq.