Yes, one can certainly find a lot of material in Nietzsche's work supporting this interpretation. But there is so much more to it. Giorgio Colli wrote that "Nietzsche has said everything, and the opposite of everything." Depending on how you pick and choose, you can construe it to mean pretty much anything you want. Which is also what enabled his sister to use her brother's work for her own nationalistic, antisemitic goals.

This is the milquetoast interpretation of Nietzsche to make him digestible for the mainstream.

Yea, he wished suffering on his friends, to forge them into beings worthy of respect. Etc. He did have an aggressive and elitist perspective. Ayn Rand's views are a decent comparison.