This is most easily seen from the mathematical point of view: the Schwarzschild metric reads: $$ds^2=-c^2(1-\frac{2GM}{c^2r})dt^2+(1-\frac{2GM}{c^2r})^{-1}dr^2+r^2d\theta^2+r^2sin^2\theta d\phi^2$$ for bodies crossing the horizon slowly, we may have $$\frac{dt}{d\tau}=\frac{1}{\sqrt g_{00}}=(1-\frac{2GM}{c^2r})^{-1}$$ The radius of a black hole is its Horizon, and this radius is the Schwarzschild Radius, which equals $r=\frac{2GM}{c^2r}$. So at the horizon, the ratio of the coordinate time and the proper time is infinite, which means you would measure the bodies' time to slow down by a factor of infinite, which means you wll see them stop at the horizon.

This is most easily seen from the mathematical point of view: the Schwarzschild metric reads: $$ds^2=-c^2(1-\frac{2GM}{c^2r})dt^2+(1-\frac{2GM}{c^2r})^{-1}dr^2+r^2d\theta^2+r^2sin^2\theta d\phi^2$$ for bodies crossing the horizon slowly, we may have $$\frac{dt}{d\tau}=\frac{1}{\sqrt g_{00}}=(1-\frac{2GM}{c^2r})^{-1}$$ The radius of a black hole is its Horizon, and this radius is the Schwarzschild Radius, which equals $r=\frac{2GM}{c^2}$. So at the horizon, the ratio of the coordinate time and the proper time is infinite, which means you would measure the bodies' time to slow down by a factor of infinite, which means you wll see them stop at the horizon.