That's kind of the definition of the event horizon. You cannot be 'safe' once you're inside. All paths lead to the event horizon. No matter which direction you point, you're pointed at it.
I am not too knowledgeable about black hole physics, but it was my understanding that there's nothing locally interesting about event horizon: it's just the point of no return that doesn't change much for the local observer. Your definition of the event horizon make it sound more locally important.
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.
All paths point singularity-way but a cone will also see a false image from in falling photons. That cone will get smaller the further in you fall. That doesn't mean you aren't pointed at the singularity, only that some photons are going faster than you. It's like saying that because some traffic on the highway is passing you, you're actually going backward.
All paths inside the event horizon lead to singularity. Full stop. This is reinforced by the Penrose diagrams you mention.
