There probably isn't as much latency as you think. Remember it's the military. It's probably one hop to the satellite, and one hop back down to the drone, and military satellites tend to be in reasonably low orbits, so you wouldn't even have the light-speed latency of a trip to the Lagrange points (Or HEO) and back.
Edit: How do you figure 26,000 miles? You're assuming the satellites are in MEO, which isn't a valid assumption. Also light travels 26,000 miles in like .13 seconds, so even if it was traveling that far .5 second latency is about twice what you'd be seeing.
You're looking at the whole thing backwards. We know they're doing it. The question is how? My thought is that it's perfectly possible that they're bouncing off a series of LEO satellites, or that they're taking a fibre hop to Europe and bouncing a satellite from there.
Or alternately, they're flying with much greater latency than you'd think. It's not like they're dog fighting at high speeds or anything.
Edit2: Lot of people are talking about switching latency, and that's really only a factor in two cases:
The switch is over utilized
There are too many switches in the circuit
In this case, I would be very surprised if the latency was appreciably increased by the switches. It's far more likely that latency would be increased by encryption overhead or actual light-speed restrictions than by switching hardware.