hmmmm. It's a well known situation about the L and R sounds. If you learn to hear and pronounce the difference before you are about 3 or 4, you're fine, but it is very hard after that. I've even heard of some parents getting surgery on their kids tongues (trimming the connection between the tongue and the floor of the mouth) to help them with this, which is XXXXing stupid because the difference is where you put the front of your tongue. As you and Clod say, it is to do with training your brain.
As to why your friend gets them consistently inverted, I don't know of any "official" explanation, but I think yours is a pretty good one.
I'll keep this in mind and if I learn anything, I'll get back to you.
Final word of advice: never ask a Japanese person to lend you a "lead pencil". Just say "pencil".
