Well, booboo, there is something called erosion-- a process to which you yourself have referred. See, what happens is that as water ( in this case ) flows across the ground it moves loose particles of earth. Eventually, this carves a channel. This, for the doubters, can be demonstrated with a waterhose and some loose soil, or, even better, with a mud puddle on a rainy day and a pair of bare feet. Now, imagine that this channel of water flows though a bit of earth that is slowly rising. If the rise of some portion of the earth is greater than the rate of erosion, then you will get something like what you propose-- that the river gets damned, except that it won't be damned but diverted to another path. Off the cuff here-- the geologists can confirm or contest this-- the Grande Canyon shows ample evidence of there having been such diversions. Now, case two, if the rate of uplift is equal too or less than ( or averages out to such ) the rate of erosion, then the river will cut its channel right though the uplifting ground, essentially remaining in the same place relative to some fixed reference point. Think about cutting a ball of dense clay with a knife. You can push the knife down though the clay, but you could also mount the knife in a fixed position and push the clay up through the knife. If the upward push is fast you'll break the mount but if the uplift is slow the knife cuts right through.
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