10 or 15 years ago that sentiment may have been accurate, but hasn't jhp ammo come a long way?
Bonded bullets and better construction have increased the reliability of expansion and weight retention. But .380 is still .380, meaning that even with the advantages of better hollow points not much can be done about penetration. As evidenced by this thread, different shooters have subjective requirements for what they consider to be adequate penetration. There's nothing wrong with that.
After a lot of reading, I chose FMJ for my LCP. My primary reason was that I could easily buy and shoot 200 rounds, which is my minimum before relying on a firearm and a brand of ammunition. It would have been cost-prohibitive to go with more expensive JHPs in my case, and my opinion boiled down to that extra money buying me no particular advantage, and possibly a disadvantage since I put penetration right behind shot placement in what I look for in a defensive gun.
A note of caution on one brand mentioned, I did try the "+P" Buffalo Bore .380 cast rounds. They were a blast to shoot, but were unreliable. In doing further reading, I found that there were no +P standards for .380 and that Ruger does not recommend using higher rated ammunition in the LCP.
Go with a JHP if it makes you more comfortable, but keep in mind that even if there are varying views of penetration vs. expansion, shot placement and reliability should be at the top of the priority list for a defensive gun and ammo. Plan to test whatever you carry to your satisfaction.
ETA: Hey Luke, maybe this would be a fun challenge when it eventually warms up again. Pocket .380 to a 2-liter bottle at 50 or 100 yards!