In fact, I know that as a local observer falling into a black hole you can still see some of the outside world after falling into the event horizon (by looking "behind you"), you just can't send anything back. This also seem to contradict the statement that all paths point inside (or I may misunderstanding something).
Edit again: I did some research and it looks like that while parent's comment may be true for simplified model of a black hole, it is conjured to be possible for rotating black holes where you can stay inside. Also Google "penrose diagram kerr black hole" for some weird physic if you want to follow this rabbit hole. Keep in mind that I'm not a physicist and this is my understanding after 40 minutes of watching YouTube and Wikipedia.