It is possible that River was able to see Rory and Amy. The Vortex Manipulator is much less powerful than the Tardis, so it may have caused much less interference with the paradox period than the Tardis would have.
I think of it like a non-newtonian fluid. The Tardis is like a fist hitting the fluid, and not being able to get through. But the Vortex Manipulator is like something gently pushing into it, sliding through with ease.
As far as fixed points go, the Tenth Doctor proved that they could be changed (though, that one brought about a tragedy). So, I have to assume that it wasn't simply that Amy and Rory were fixed points. I think that it's also because in attempting to see them, the Tardis would have set off some type of chain of events though the warps in time the angels had caused. After all, he didn't actually tell anyone that it was impossible to see them - He just said it would rip New York apart. That tells me that the fixed point can be changed, but to do so would bring about such negative consequences (namely, the destruction of a city with a huge number of people in it) that the risk isn't worth taking, even to see them again.