If they were accepting students for Feb to “game” admissions stats, they would likely be doing less to draw attention to these students. Midd has special February convocation, the Feb graduation on skis, etc. My feeling is that, as you wrote, they’re staggering admissions for different technical reasons, and they created the entire Feb cohort culture to compensate for the inconvenience of having to wait until February to start. Since their acceptance rates include the Feb admits, I would guess that they include the Feb admits in the rest of the stats.
I don’t know whether there is a similar culture for spring admits at other colleges.