That seems far fetched. 1000' is a long way at 5mph. The number of engines doesn't matter. Each car has its own brakes in an emergency. Cut pressure in the line and every car will brake itself. Perhaps they meant situations involving hills, not uncommon for ore trains heading from mines.
There's a whole sequence of events behind this, from the work to remove slippery leaves from rails, to the sand applied during braking if wheels are slipping, to the IT systems and management processes identifying why the train didn't have any sand. It's a fascinating 151 page report.
https://www.gov.uk/raib-reports/station-overrun-incident-at-... (PDF report linked at the bottom).
Counting pixels, the distance covered from 10mph to zero is about 350 feet. With this distance for a lightly loaded passenger train, 1000 feet doesn't seem impossible or even unreasonable for a heavy freight train at 5mph.
Drivers likely could not give an accurate estimation for how many feet it takes to do anything on the road, such as come to a stop in an SUV going 50. Given the extreme mass of a cargo train, I wouldn't be surprised if the distance figures sounded high.
Isn't knowledge of stopping distances for vehicles at various speeds and different road surface conditions a requirement for obtaining a driving license? (At least, in the UK I believe it is, and I think the Highway Code tables probably over-estimate these distances for safety purposes)
That said, I think often the bigger problem is people not realising especially in more unusual conditions (like snow in much of Britain) quite how much longer braking distances become.
Air brakes, once pressurized, don't take much to maintain. Relatively small pipes work on even very long trains. You can add cars all day without increasing the steady load on the compressor. A longer train will take longer to pressurize, but once there it would not need the compressor to run constantly. Air is also not as dangerous as running large electrical cables the length of a train.
This lets them start easier/quicker from a stop, as they don't have to re-air the entire train and less wear on the brakes of the trains in the front of the train as all the cars start braking at the same time. This is particularly useful for trains that have to start on a hill as taking minutes for your brakes to fully turn off can complicate things.
That said, I think an emergency stop (air loss) would stop it faster.
I once learned in a physics class that weight has nothing to do with the stopping distance, but rather the steel on steel friction coefficient.