No, it's four.
When you hear "3" it's because that's how many NCAA titles volleyball has won.
However, they won the AIAW national championship in 1981 when that was THE championship, since the NCAA was late in recognizing national championships in many women's sports. There's nothing illegitimate about it. It's not some kind of made up national championship after the fact like other schools we know, do.
When you hear commentators remark about UT's 3 national championships, you'll always hear them add the word "NCAA Championships." But it's not really accurate in the most pragmatic sense. That's a real championship. The banner hangs in Gregory for a reason. It's officially accounted for in every Texas source you can find, and it should be.
When Mick Haley is cited regarding his national championships, he's credited with 4 - 2 at Texas and 2 at USC, with one of them being the AIAW championship in 1981.
Anyway, it's a pet peeve of mine. It diminishes the UT volleyball program slightly in a way that's undeserved.
Congrats ladies on number 4!