NFL doesn't have a very good track record on the medical front. https://www.pbs.org/wgbh/frontline/film/league-of-denial/ If chiro provides cheap short term care at the expense of the player, that sure does sound like a great deal for the business that is the NFL/NBA.
You're just making things up. It's not "at the expense of the player" These players are in peak physical fitness. If they want to go to any kind of doctor they can as they have medical insurance and they are all multi-millionaires.
Documentary is about concussions, I saw it years ago. Has nothing to do with the player's preference for chiropractic.
Player likes chiropractic because he believes it makes him perform more optimally, you inserted/made up this concept of the NFL pushing chiro to save money "at the player's expense".
Pro-athletes preferring chiro is a strong counter-signal these "skeptic" articles.