I think it's important to note that this data doesn't say "hard hit balls are not more likely to be base hits". The hardest hit balls are usually line drives, which have a much higher BABIP (~.730 depending on which article you read) than ground balls (~.240) and fly balls (~.150). This data says "Fangraphs hard hit% doesn't influence how likely base hits are". That arises because they normalize it to the batted ball type. In other words, they decide whether it's a fly ball, line drive, or ground ball, and then assign a soft, medium, or hard rating, such that you've normalized out the enhanced BABIP from line drives. Once you get past that, I think all the factors that Jersey mentioned come into play.