Okay, let's just think for a second here.
You're telling me that there's an alien race (or shadowy government experimental organization) that can figure out craft that are capable of:
1. Interstellar travel (if aliens)
2. Traveling at insane speeds through atmosphere without causing a sonic boom or affecting the surrounding air in any way
3. Moving at these speeds without any standard means of propulsion known to man
4. High level stealth technology so they weren't picked up on radar or anything
And they want to observe, but they CANNOT figure out either:
1. Some form of active camoflage, or anything else that would prevent them being observed with the naked eye or some sort of video camera
2. Cameras/radar/sensing apparatus that allows observation from range so they don't have to fly close to the ground to look at the jets
And instead figure the best way to observe silently is to zip back and forth across the air like idiots instead of parking somewhere they can't be seen and watching.