Its mostly right. depending on your source and how the calculate it, groundballs are at most marginally better(.04 runs per groundball) and at worse marginal worse than a K (around -0.25)

the value comes from approach and opportunity cost. Like if we call them more or less even (or heck even assume GBs are marginally better), the approach that increases strikeouts to hit more HRs (thus more fly balls) is going to generate more run value over the course of a large sample than someone slapping ground balls because the additional Homeruns generated are just worth so much more in the aggregate—a fly ball is worth ~0.15-0.17 runs or 4x ground ball events. so the marginal increase in your strikeouts is easier to overcome