I took one of my samples apart to see how it was made. Essentially it is a sleeve bearing fan with a POM side bearing to keep it running smoothly. Like all sleeve bearing fans (and this includes variants like FDB, HDB, etc.), the shaft is held in place by a retaining disk. Holding the head of the shaft away from that disk is a magnet. This is pretty common.
Now, if you can exert steady pressure on the impeller, eventually the head of the shaft will snap through the retaining disk and get your blade assembly (the impeller) free. But once you have re-oiled it, the head may not snap back through the disk. If you get it back in, the magnet should hold the shaft in place. Should.
I have pulled the impeller off a Sickle Flow (a sleeve bearing fan) and when I put it back the fan still ran. So it is not impossible.
But that Jet Flo should run without lubrication. Why not just wipe off the excess oil and let it run?