"These images give some idea of how close aircraft can seem and still be at least 1,000 feet apart"
Nonsense! Those are professionally done air-to-air photos, and I say that as a shooter with probably four dozen--never counted 'em--Flying Magazine cover shots to my credit in the late 1960s and '70s.
Those aircraft are -way- closer than 500 feet, even.
When did this become the Professional Passengers Rumor Network?