[chris (OP)]

A caller to the Ask! the Naked Scientists phone-in programme today spoke of the Bosut River that, he said, apparently sometimes flows backwards.

This sounds fishy to me! Anyone heard of this?

[evan_au]

Could they be talking about a "tidal bore"?

This is where the incoming tide overcomes the outflowing river, producing a wave that travels upriver.
Some people even go surfing on them!

See: https://en.wikipedia.org/wiki/Tidal_bore

[evan_au]

As I understand it, the tidal bore does not actually reverse the flow of water in the river...

The tidal bore occurs in the lower section of the river, near the sea, and the speed of water in the river is pretty low, here.
The shape of the bay channels a peak incoming tide into a surge, which creates a wave.
The velocity of a wave exceeds the velocity of the water, so the wave propagates upriver, even though the water in the river continues to flow down to the sea.