This one annoys me, because of it's ether/or proposition when it is more of a and/or function.
Yes, water including rivers cuts through rocks in more than one way. For example, Ph differences in the water can cause chemical weathering of the rock. In general these effects happen slowly and need to be persistent for any measurable effect.
But to deny the absolute power of a raging torrent and the amount of physical landscape change it is capable of in just moments is absolute folly. A swift river full of sand and chunks of rock can act like a water cutter or a sand blaster.
https://en.wikipedia.org/wiki/Missoula_Floods are a testament to the power of water.