Someone who's hyper independent would prefer solitude and would likely have problems with relationships for a number of reasons including being really out of practice. And not having any reference point for understanding what a secure attachment looks and feels like.

You can have a significant preference for being alone, require a great deal of quiet time and still suffer from social isolation.

It's all interconnected, we're not designed to live a life alone.

Having said that I still wish people would stop approaching me when I leave the house :/