Most users on /r/AskAnAmerican don't seem to consider American friendliness fake:
https://old.reddit.com/r/AskAnAmerican/comments/ehe25w/why_a...
https://old.reddit.com/r/AskAnAmerican/comments/1k7sfbv/so_w...
https://old.reddit.com/r/AskAnAmerican/comments/1nq71lc/why_...
The US is a big place. There isn’t one “American culture”. If someone in one part of the country says we should get drinks sometime they’re just saying a nice thing. In another part of the country, that means “this weekend”.