"If berths in the selected other bowl games remain available after those teams have been identified, the highest‐ranked other teams, as ranked by the committee, will fill those berths in rank order."

Note that there is nothing that says top 12 are qualified teams and at large teams can be selected from that pool of eligible teams. Instead, it specifically states that remaining spots are filled by teams "in rank order". What you are stating is how things used to work under the old BCS system, but it hasn't worked that way since they switched to the 4 team playoff.