Yea, if you listen to the ATC audio, you can hear that in addition to the normal high workload of handling both ground and tower, this guy had an emergency aircraft on a taxiway to deal with, too. A lot of holes in the swiss cheese lined up, but one of them clearly is ATC workload.
Perhaps in a scenario where there is an active emergency and one controller, protocol should be that ground and air frequencies are combined.
That would have given the jet a chance to hear the truck cleared to cross the runway they were landing on.