My sister has the dark red hair I think you’re talking about — at a glance people would call it auburn, but when the light catches it you see it’s really a dark red (not orange). My extended family going back generations has hints of this, but in everyone else it’s mostly been a red tint to another colour. I don’t know anyone else who has actual naturally red hair.

She gets the flush cheeks and freckles of the traditional orange redhead too; that seems to go with the hair, as nobody else in the family has that complexion (and yes, she’s my genetic sister).

Just a single anecdote, but I hope it helps.