[Al-Khwarizmi]

Examples like that are parsable because they are similar to what we would call, in programming, tail recursion (i.e., recursion that doesn't really need recursion). It's true that you can embed an infinite number of subsentences ("John, my friend from high school, who married your cousin, Mary, who had an affair with the bartender, Jack, who hated his sister, Lisa, who was a fan of Lady Gaga, is coming over for dinner") but you only need two "stack frames", one to remember John and the other for the rest.

The middle part is basically equivalent to saying "Mary had an affair with the bartender, Jack. Jack hated his sister, Lisa. Lisa was a fan of Lady Gaga". My intuition is that it's parsed basically as separate sentences. Once you finish one of them you can just forget it, you only need to remember John (as there is more information about him in the end). Sentences where you need to remember more elements (i.e., you actually need unbounded recursion) become unparsable in real time as my previous example.

Of course, I don't have scientific evidence to back the things I'm saying, it's just intuition, but the same can be said of the Chomskyan theories.