A friend of mine who will remain nameless at this time (Wayne) does a lot of traveling down to the States and he sent me this article ...., which you might want to read if you're taking an aeroplane [sic] sometime in the future:
If you are asked to leave an airplane after boarding, or if you are not permitted to board the plane, the first thing you should say is "Am I being denied boarding?" The second thing is "give me your written denial of boarding compensation statement".
Once you do that, the odds are that you'll get on the plane. If you aren't boarded, remember that the compensation amount is calculated on the posted one-way fare to your destination, not on what you may have paid for it.
If you have been legally denied boarding, don't accept a flight voucher unless the amount of it is twice the cash compensation you are owed.'
If you have been issued a boarding pass, the airline is legally obliged to carry you. There are certain exceptions, but basically, if the plane is going and you have a boarding pass, they CANNOT deny you boarding. Legally. If they do, they must do certain things. I'm gonna link to the law below.
The penalties for denied boarding are substantial, though not as substantial as they ought to be, since the law was written decades ago. They include substitute transport to get you to your destination within 2 hours of your original reservation, on any available flight, PLUS financial compensation in cash (not travel vouchers) handed to you before you leave the gate area.
The airlines have been playing fast and loose with boarding passes and with overbooking for years. They have come to rely on getting volunteers to accept a voucher worth a fraction of the money they would otherwise be owed for denied boarding. Clearly the gate crew in Chicago was so poorly trained that they thought they could bump a passenger who had a boarding pass (but maybe he didn't....more on that below) but who had boarded the plane.
Now, here's the thing about boarding passes. They are documents issued by the airline. Not a QR code on your phone.