It isn't the same principle. Firstly, coastlines are more jagged because they are hit by waves perpendicularly, while rivers are shaped by water flowing along the banks, smoothing them. Secondly, the borders are typically defined by either the thalweg (greatest depth) or median line, either being smoother lines than the banks. Thirdly, river borders are then in practice defined by measuring the coordinates of particular sample points along the idealized line and then using straight lines or simple mathematical curves to connect these, forming a simple non-fractal boundary.