That's true only during the BCS era, which is fairly recent. Before that they had "New Years Day" bowl games. Rose, Orange, Cotton, Sugar. That was the equivalent of the final four. And BC went to three of them. Much later the Fiesta became big. So yes, it is the measure of excellence and they went three times to our 1.
Actually, four times (Cotton 1939, Sugar 1940, Orange 1942, Cotton 1984), only one of which occurred in the last 70+ years, and not since Reagan's first term.
That 1940 season was marked by The Lou Montgomery Story, which is objectively disgusting, and pretty much the antithesis of what college sports are all about.
Conversely, 90 miles away, another institution was one of the first in the nation to admit Japanese Americans coming out of internment camps, and freely welcomed them to play on their sports teams.
Such a fine institution, that Boston College.