The Bracket is out, and once Virginia was announced as the final 1-seed, I realized Wisconsin may be in a unique position. The Badgers beat both Florida and Virginia during the regular season, and have the possibility to beat both Arizona and Wichita State in the tournament. If they do so, they will have beaten all four 1-seeds this season. I had to find out if anyone ever has. There have been 116 1-seeds since the field expanded to 64 in 1985. Naturally, all the 1-seeds are excluded by virtue of being unable to lose to themselves.
It turns out there have only been 2 teams that have 4 wins against 1-seeds in the same year, and they're both Arizona squads. In 1997, the Wildcats beat North Carolina twice, Kansas, and Kentucky en route to the national championship. They never played Minnesota, the other 1-seed. In an even crazier 2001 season, they came within a game of doing it: they split 2 regular-season games against Illinois before beating them in the tournament, split regular season-games against Stanford, and beat Michigan State in the Final Four. The last 1-seed was Duke, who they lost to in the National Championship. They played 7 games against the 1-seeds that year!
There have been 7 teams with 3 wins against 1-seeds (what was it with the Wildcats those 4 years?): 1985 Illinois 1985 Georgetown 1986 Duke 1991 Duke 1992 Southern California 1992 Indiana 2000 Arizona
The distribution falls off rapidly after that: there have been 64 teams with 2 wins against 1-seeds and 352 with 1 win.
The all-time leaders contain no surprises. If we assume that most of the 1-seeds come from historically "power" conferences, being in the same conference provides more opportunity over the course of a season to play against them. Going deep in the tournament doesn't hurt either.
On the flip side, Wake Forest has the dubious honor of most losses to 1-seeds in a year. In 2002 they also played 7 games against the eventual 1-seeds. They went 0-7, losing to Cincinnati and Kansas once each, Maryland twice, and Duke 3 times. There have been 16 5-loss teams and 73 4-loss teams. In terms of all-time futility, NC State takes the cake. Since 1985, they have a paltry .114 winning percentage against 1-seeds:
So if the Badgers pull it off, they'll be the first in the 64+ team era to do so.
Stats courtesy Sports-Reference.