According to Wikipedia it started out as a mod, Valve asked them not to give it a name too similar to their own Half-Life Source, then later Valve approached them and suggested a commercial release!

In Valve’s case it’s just a smart move both for PR and business. Black Mesa isn’t competing with any of their products since I’m sure not many younger people are super interested in the original. In fact the remake might drum up interest by some people to play the original. And it’s sold on Valve’s platform, giving them a cut. Win win.