I don't claim to speak as an expert on the subject...so I might be wrong...but I don't think they really have to pump it normally...the pressure it is under pushes it up.
But I have wondered if they could suck it up at the source...but that is a lot of weight to yank up from a mile. Won't even begin to try and figure out what kind of pump you would need to pull that much liquid straight up for a mile.
The suction head would be only the height of the pump above sea level, probably ~20m. You’d likely get a lot of sea with the oil, but that can be separated out, Associated gas would put more strain on the pump than would the suction head.