I've found at least three cases where this happens; it does not appear to be common. The river may be near the coast, but the F3 screen does not show the river as connecting to anything resembling a river (and also usually shows adjacent ghost beaches), and in one case is completely enclosed by the ocean. This is different from the many rivers that merely have an unusually large delta that extend into the ocean, but do contain a sort of river bank. Note that they all involve warm oceans since they made it easier to spot the river.

(Seed: -4753858570600020860; Pos: -7187 84 1506)

(Seed: -753111143593067491; Pos: -3721 107 787)

(Seed: 93366035475932059; Pos: -7187 84 1506; Also a bifurcated small warm ocean at -5775 92 -4749 (not shown))