That's an urban legend. In real life physics, the traveler is being pulled forward by the black hole's gravity, faster and faster, and as it covers the last few miles it's traveling very close to light speed and crosses the last few miles in a tiny fraction of a second. The time dilation is not enough to cancel the increased speed. There's no wall of molasses. An object falling in goes faster, not slower. Objects falling into the black hole do not actually hover just short of the event horizon, despite appearances.
