Precisely. If you struggle to hit home runs it's because you aren't as good a hitter against that side.
Garrett Jones:
16 HR in 94 total Hits against Lefties. 17% of his hits are home runs
74 HR in 417 total Hits against Righties: Guess what that is? about 17%
His power is actually exactly the same against lefties as it is against righties. He's just a worse hitter against lefties in general.
There's no factual basis for power splits at all, barring switch hitters of course.