Just for context, the Wikipedia line in question states:
My response to this is that whoever wrote this doesn't really know what they're talking about. Some of the early tournaments the games were indeed held on campuses (including in 1942 UK played in New Orleans in Tulane's Fogelman Gym which directly contradicts the claim above.) But by 1943 the sites of the East and West regionals moved to Madison Square Garden in New York and Municipal Arena in Kansas City, MO respectively, so if hosting integrated teams on campus was an issue, it was moot because the games were not being held on campus after 1942.
These sites remained in place throughout the remainder of the 1940's and early 1950's until 1952 when the locations expanded (from 2 to 4) and changed to include a mix of municipal and college arenas. (for example the regional sites in 1952 included Raleigh, Chicago, Kansas City and Corvallis Oregon with the Final 4 in Seattle). Soon after the gambling scandal made it so that the NCAA would not hold their Finals in the New York metro area again (until 1996 when UK beat Syracuse in the NJ Meadowlands.)
But as I mentioned, the main reason why this is inaccurate is because there simply weren't many (if any) integrated teams participating in the NCAA tournament in the early to mid-1940's.
Below is the list of teams participating in the NCAA tournament. I know that by at least 1950 there was at least one integrated teams in the NCAA (CCNY) but I don't know if any others were prior to that.
1939 - NCAA Field
Oregon *
Ohio State
Villanova
Texas
Oklahoma
Utah State
Brown
Wake Forest
1940 - NCAA Field
Indiana *
Southern Cal
Colorado
Duquesne
Rice
Kansas
Western Kentucky
Springfield
1941 - NCAA Field
Wisconsin *
Washington State
Arkansas
Dartmouth
Pittsburgh
North Carolina
Wyoming
Creighton
1942 - NCAA Field
Stanford *
Rice
Colorado
Dartmouth
Penn State
Kentucky
Kansas
Illinois
1943 - NCAA Field
Wyoming *
Georgetown
DePaul
Dartmouth
New York Univ
Texas
Washington
1944 - NCAA Field
Utah *
Dartmouth
Ohio State
Iowa State
Temple
Pepperdine
Missouri
Catholic
1945 - NCAA Field
Oklahoma A&M *
Ohio State
Kentucky
New York U
Arkansas
Oregon
Tufts
Utah
1946 - NCAA Field
Oklahoma A&M *
North Carolina
Ohio State
New York U
Baylor
California
Harvard
Colorado
1947 - NCAA Field
Holy Cross *
Texas
Oklahoma
Navy
Oregon State
CCNY
Wyoming
Wisconsin
1948 - NCAA Field
Kentucky *
Holy Cross
Michigan
Baylor
Columbia
Kansas State
Wyoming
Washington
1949 - NCAA Field
Kentucky *
Oklahoma A&M
Illinois
Yale
Villanova
Wyoming
Oregon State
Arkansas
1950 - NCAA Field
Bradley
Ohio State
Holy Cross
North Carolina State
UCLA
CCNY *
Baylor
Brigham Young
By 1950, for sure CCNY was integrated with Ed Warner, Leroy Watkins and Floyd Layne. Before that, I'm not sure. If anyone can verify that any of those earlier teams were integrated and that those black players played in NCAA games, I'd appreciate knowing it.
One thing to note is that 1948 was an important year in terms of integration because any barriers (formal or informal) which might have been in place to prevent black players from participating in post-season tournaments was banned. This came via the US Olympic Committee which decreed that any organization that participated in banning black players would not be invited to participate in the Olympic trials. (And indeed this helped pave the way for Don Barksdale of the AAU Oakland Bittners to be named to the US Olympic team.)
The small school NAIB, which did ban Indiana State (coached by John Wooden at the time) in 1947 from bringing a black player (Clarence Walker) to their tournament had to relent and allow Walker to participate in the 1948 NAIB tournament. I know that a lot of UCLA fans like to give credit to Wooden for the change (and I have no doubt that Wooden was an advocate for allowing his player to participate) but it was really the US Olympic Committee decision which forced the NAIB (and in effect the NCAA as well) to open their doors to black players participating in these tournaments.