Realize that FB in OOTP is Fly ball outs, not fly balls.
I went to a script that runs through each plate appearance in a year for a 32 team league, and tabulated balls in play for every pitcher, as well as HR. I took all FB/PU/LD (because LD include HR) and then matched pitcher movement rating with their HR/FB.
If HR/FB is essentially normally centered on a league average, the correlation between movement and and HR/FB should not exist (or be, at best, very small).
So I ran correlations for all pitchers who saw at least 30 balls in play, then 100 balls in play, and 200, 300, and 500. The correlations started at -.34 (home runs per fly ball went down with increased movement), and as sample size went up the correlation went up to -.63, which is a pretty solid number and suggests that movement reduces HR/FB.
Code:
BIP Correlation
30 -0.34
100 -0.4
200 -0.51
300 -0.58
500 -0.63
This makes sense given what Movement is in OOTP (the result of which is directly stated in the user manual), but would not seem to correspond to the real baseball idea that HR/FB is essentially luck.