@flyflyfly
I went back and listened to the original audio to get a timeline on the Gulfstream which was a G-IV. In real time from when the pilot acknowledges "no delay" until they respond to the take off clearance canceled it's about 38 seconds. From their "no delay" until when I reasonably think they would have reacted to the "cancel clearance" but didn't verbally respond it's about 28 seconds. I went back and listened to the ground freq to listen for their taxi route but couldn't find it. Looking a the airport diagram I'm assuming they left from intersection M as had several previous departures. If that's the case, from M to J, and given the elapsed time, I would guesstimate their ground speed to have been 45-55 knots if not greater. Not anything too horrible but still an unexpected event given the "no delay".
I agree that the gear issue wasn't necessarily a serious danger to the safe flight of the aircraft and given that they had declined a fly by to double check the gear, the declared the emergency was out of an abundance of caution. Also having listened to some of the other audio, runway 12L was in service, and being used by several aircraft immediately preceding the incident. I still feel like this is an all too common occurrence of ATC feeling pressured to get an aircraft out before an emergency aircraft potentially closes the field for a period of time, and I feel this is what can one day lead to devastating results. I know time is money when it comes to the airlines but it's hard to get either back should the worst happen. Again just playing devils advocate to all the what if's, which I could go on about further but I think this dead horse has been beaten enough.