Agreed with Rat 5 - how did they get it out if a tug couldn't get it out in the first place? Lugs on the mainwheels have been mentioned so I assume someone got a couple of JCB's and some rope?
Also, on the whole who did what - from my understanding it is fairly common to call for start and taxi as you're being pushed back (ie. before you've been pushed onto the grass) and even then, the crew are going to be too busy looking forward to be concentrating on exactly how many cm they've been pushed back (no reversing cameras on an A320) unless there was a bump as they went over the edge I guess.
Either way, as it is illegal to publish (publically re-broadcast) ATC recordings in the UK it is very unlikely anyone external would be recording the RT (liveATC.net etc.) and thus we'll never know the exact series of events.