My Ph.D. dissertation was on data acquisition and reconstruction techniques for MRI. I've logged hundreds of hours operating high field scanners like the one shown, and dozens of hours being scanned for various research studies. I've also (carefully) hauled a variety of strange things in and out of scanner rooms. Most of the tools we used were non-ferrous, and we had to be extremely careful with the few ferrous pieces of equipment we had to use. The magnetic field does drop off rapidly as you move away from the scanner, so objects more than 10 feet or so away are unlikely to be pulled in.
The electromagnets which are only turned on during operation (used for the gradient fields and for shimming the main field) are insignificant in magnitude compared with the main field. The main field is powerful enough to lift a ferromagnetic chair off the floor if the chair gets close enough to the bore without the gradients being active.
They're not magnetic enough to pull a chair off the floor or things across the room (as the story indicates) when they are not in operation. You can walk around the room with your watch on (for example), but if they fire it up and you're in there with it, it's destroyed.
Just look how close they have to get the steel oxygen bottle to the center (in the video linked above) before it moves. It's almost inside it already.