I remember browsing "fact" sites as a youngling and seeing this one pop up every now and then. Rationally, I thought there must have been a number of accounts on this event, but I was, and still am, not sure what the truth behind this event is.
You are right to be skeptical It's a pretty unbelievable event. This one though actually appear to be true. In 1811 and 1812 a series of earthquakes in the area of New Madrid Missouri caused the river to flow backward.
The first quake was on Dec. 16 1811. The USGS estimates the magnitude to have been around 7.5. Some eyewitness accounts suggest that the Mississippi flowed backward for several minutes during this event. The earthquake was followed by several aftershocks of magnitude around 7.
The main event came on Feb 7, 1812. An earthquake possibly as strong as an 8 in magnitude caused several miles of the river in the vicinity of New Madrid to flow backward for several hours. Temporary dams and waterfalls created by the earthquake affected the river's flow for several days. The town of New Madrid was destroyed.
If you want to mince words it can be argued that the river only "seemed to flow backward." But I think seeming to flow backward and actually flowing backward are about the same so far as the story is concerned.