It's not just about how random the hookup is. There are plenty of guys who have whored around for years and remain negative because they only engage in low risk behavior (mutual j.o. and oral sex) or use a condom EVERY time for anal. That's not foolproof, but it dramatically reduces the risk.
Just as importantly, there are lots of people (men and women) who have contracted HIV through serial monogamy or simple monogamy, because they assumed that they were safe because they knew their partner. However, if one's partner is out getting gang-banged in the bathhouse on the DL, then trusting them can prove fatal. We tend to distrust people we don't know and trust those that we do, but sometimes that trust is misplaced.
In other words sometimes it's more about what you do than it is about who you do.