Since 1975-1976, this is the list of NBA teams who have won the title without a player being named first or second team NBA All-Defensive (not necessarily a big man).
1977-78 Washington Bullets (Bob Dandridge was first team All-Defensive the following season)
1980-81 Boston Celtics (ML Carr, Larry Bird, and Kevin McHale were future or former selections)
1994-95 Houston Rockets (the previous and following season were among the 9 selections for Hakeem Olajuwon, the previous season's Defensive Player of the Year)
2005-06 Miami Heat (Shaquille O'Neal and Dwyane Wade were former and/or future selections...so were part-timers Gary Payton and Alonzo Mourning)
If you want to narrow it even further, then only one team (the 1980-81 Celtics) has ever won a title without a player who was either first or second team All-Defensive in that season or the previous/following season. Wierdos.
If you think I'm inviting comparison to the argument that the Celtics need a player drafted in the top five to win a title, you'd be right.