No-one said anything about the president or the NSA being involved. There are tons of ways this can work. And it actually happens.

Just once you're flagged and are inside The Machine you get detained upon entry whilst they confiscate your devices, try to see where you've been etc. Lookup the wikipedia page of Laura Poitras who for years lived in Berlin due to USA government surveillance. And this started way before her involvement with Snowden as a filmmaker.