I'll chime in as someone from the US who attended a public school and took a calculus class that used a university level text and did exactly as you described. Color me surprised when I arrived at university only to encounter that same book in use for the calculus course sequence.

The person you're engaging with here clearly has an overly generalized view of the US educational system (and is overly confident in it). It's not surprising that there's a bit of variance - the place is rather large after all.