Can big snakes really be that strong?

You'd be surprised at how strong snakes are. Even small snakes (non-constrictors) have a strength that is amazing. Think of how well and how long they can hold a pose hanging from a tree branch, with part of their body held horizontal. When it gets to constrictors, like pythons, they hold their prey until it stops breathing (they don't have the poison of other snakes). I'm not sure that they could crush your ribs - there is a limit there - but they could hold you so you can't breathe, and that's strong enough for most purposes.