I am particularly sensitive to this, being involved with MDA. I understand that there used to be weekly attempts for Palestinian ambulances to cross the green line through checkpoints into Israel either "empty", that is, with no patient, but full of explosives, or "full" with a mock patient, and explosives packed everywhere not obviously visible. There is a video on youtube of a robot removing a cot mattress filled with explosives.
Since these attempts have started, the Israeli army has a policy of not allowing Palestinian ambulances through checkpoints, rather transferring care to an MDA ambulance at the checkpoint. There have been a few high-profile transfers, including an infant being transported for an operation only possible in an Israeli hospital.
Even in and around Tel-Aviv, whenever we enter a hospital complex, we must stop, and are quickly "searched". That is, the security guard makes sure they know the driver (despite the fact there are dozens of security guards and dozens of drivers, we are making daily trips, and each gets to know the other. The guard opens the side door of the ambulance, makes sure there is a patient, and checks to see that all other MDA staff are in proper uniform. This check only takes a few seconds, and is done several times a day, every time we enter a hospital, but is very necessary to Israeli security. Once we reach the ambulance entrance, there is another guard, who checks to see that we indeed have a patient, and that we are locking our ambulances.
I think in this post 9/11 world the US has every right to be anal about its borders, and based on the assumption that there is a written policy in place that was not initiated by the ambulance, they are the only to blame. I understand the media's interest in blowing one case out of proportion, but as others have said, USCBP is sacrificing the good of one for the safety of many.