To a distant observer, clocks near a black hole appear to tick more slowly than those further away from the black hole.

This statement is TRUE and describes gravitational time dilation, a prediction of General Relativity. Clocks closer to a massive object (like a black hole) run slower relative to clocks further away when observed from a distance. This has been experimentally verified and is why time appears to slow down near black holes from the perspective of a distant observer. An observer actually at the black hole would not notice any difference - this is purely a relative effect.