Rivers don't move with the plates, well, they do, but they also move in addition. I'm not an expert but you can see the California-Arizona border along the Colorado river doesn't line up with the current course in a few places:
If a river straddles a flat line you might get a kink, but that’s normal in rivers. Generally they are surprising resilient, consider the rather inaccurately name new river basically ignore a 480 million year old mountain range that’s in it’s path. https://en.wikipedia.org/wiki/New_River_(Kanawha_River_tribu...
https://www.google.com/maps/@33.9012327,-114.5227135,14.5z
Similarly, with the US-Mexico border further along the river
https://www.google.com/maps/@32.6117771,-114.7983232,14z