It seems like the only reason we care is because others say we are not. I pulled this from Wikipedia on the definition of "blue bloods":
In American college basketball, the term "blue bloods" is used in reference to National Collegiate Athletic Association (NCAA) Division I basketball programs considered to be among the most elite, either contemporaneously or historically. Outside of sports, blue blood is used as an alternative term for nobility.
Basketball media writers often debate which men's programs are considered blue bloods. The men's programs of Duke, Kansas, Kentucky, UCLA, UConn, and UNC, are often included when listing blue bloods. Indiana's men's program was historically considered one as well, though its status has waned in the 21st-century.
Regardless, historically (going back to the time when the field was not 64, and teams like UCLA basically had a cake walk to the final 4) UConn was not on the radar. Last 25 years - we are #1 and no one is close.
Maybe this will sound arrogant, but I sort of feel like we are beyond that (blue blood status). It's not that we have the most NC's or the most history, but we certainly have the best recent history. I think it's kind of funny that some (other fans, talking heads, etc.) seem to want to put down our program, but no one has come close to us this century.
Pretty cool for a school that started as an agricultural college back in the late 1800's.