That's the team that was referenced in this article earlier today:

"Up until the 1950s, the NIT was the most prestigious postseason college basketball tournament in the land. Even as recently as 1970, teams actually declined invitations to the NCAA Tournament to play in the NIT."

In 1970, #8 (AP) Marquette was 26-3, but was given an unfavorable seeding and region. In protest, Marquette turned down their NCAA invite and played in the NIT instead, where they defeated UMass, Utah, LSU, and St. John's en route to the NIT Championship.

McGuire became the last coach to turn down an NCAA Tournament invite in favor of the NIT. Following the 1970 season, the NCAA mandated that if a team was invited to the NCAA Tournament they must accept.

McGuire later led Marquette to the 1977 National Championship. Some Marquette old timers (and occasionally their local media) mention a claim to a share of the 1970 National Championship.