2 or 3 minutes, that is the question. However there maybe a greater point here.
Whilst the cause of the A300 crash in New York last year has yet to be officially published there has been speculation that the aircraft departed too soon after the previous aircraft. Avoidance of wake turbulence is important, particularly in critical phases of flight.
Secondly, it surely it is up to the PIC whether he takes off immediately following his clearance to do so, or waites for a further period if he has any doubts. It is he that is ultimately responsible for his aircraft and passengers, not the tower controller who would like to squeeze in the next landing aircraft as soon as possible.
Thirdly and most importantly - there was no accident here. No body was hurt or injured. So whilst the finer points of aviation law maybe in discussion, safety has prevailed - the GO pilot did not allow himself to get into a dangerous wake vortex situation, despite pressure from ATC. That's a well done in my humble book