Yes, it would have been good if either of the 2 AA men or the third mechanic/recovery driver had found the fault. However, it started for both the AA men after about 30 minutes and the car did re-start for a short time (a day or 2 ) thereafter. I felt that the AA did what they reasonably could in a realistic time unlike the dealer which had the car for 11 days and could not find a fault...
In response to Jocko's recent post I was tempted to name and shame the dealers but in the end decided not to, mainly to avoid any further aggro.
Judging by the invoice, the independent garage found the problem within less than an hour by employing a bit of diligence.