I agree this isn't denied boarding. Using that in any correspondence you send in might confuse the situation.

unless you bought the replacement ticket at exactly T-45min when UA was trying to close the domestic flight checkin), I'd have still been on the phone, documenting holding or trying to force the issue with AC. Heck, I'd have done so up to the point of final boarding prior to scanning a refundable paid ticket.

After many years on FT and a good amount of travel gone wrong, my impression is that any funds spent rebuying a flight are rarely, if ever, reimbursed.