We are dealing with terms of art here, it's important to be precise about terminology. This is refused transport, not denied transport. And EU261's IDB compensation provisions, just like APPR, apply only when the airline doesn't let you on the flight because it's oversold ("If you have presented yourself on time for check-in with a valid flight reservation and travel documentation and you're denied boarding by the airline due to overbooking or for operational reasons, and you don't voluntarily give up your seat, you are entitled to"). The same page also makes it clear that the airline can refuse to transport you "if you don't have the correct travel documents".

As I said earlier, AC was incorrect to state that the OP didn't have the right documentation to match the name on the ticket, but EU261 would be no more favourable to the passenger here than APPR. The denied boarding provisions simply aren't designed to apply to airline screw-ups.