With due respect, this does constitute denied boarding within the meaning of Reg 261/2004. The Reg defines denied boarding as the situation where the carrier refuses to carry you on the flight despite having a reservation on the flight and presenting yourself for check-in by the check-in deadline or, if no deadline is indicated, 45 minutes before flight departure (se Articles 2(j) and 3(2)(a) of the Reg).
In truth, a huge proportion of IDBs occur at check-in rather than at the gate (indeed probably something like 99% of cases for passengers with baggage). Your interpretation would create a gaping hole in the protection offered by the Reg and is clearly untenable as plainly incompatible with both the wording and spirit of the Reg.