I don't get the IDB argument. To be involuntarily denied boarding you have to have met all the conditions per the tariff.
The customer did not arrive at the gate and was ready to board by -15min to departure, which is in the tariff.
End of story.

Now, there are many reasons why a customer may not be at the gate, some of their own accord, some because of someone else, and some because of the airline, but regardless of the fact, IDB boarding is a tariff issue and AC did not violate the tariff.

Was this a customer service fail? Sure sounds like it. So treat it accordingly and offer appropriate goodwill customer service recovery compensation.

But to insist on a legally defined process where no tariff breach occurred, that is stepping into an ugly grey area that could set precedence for unintended consequences down the road.