You have it directly wired to your head unit via AV inputs and still get interference? That's strange. I've heard of noise coming through using a FM modulator. IMO, its probably not the ground in the cigarette lighter. I would think Subaru would ground that pretty good. But, you could ground it yourself to knock that off the list of possiblities. It could be something with your connection to the head unit. It may be intstalled incorrectly.
I'm only basing my opinion on my XM setup. I have the tape adapter going to the OEM unit with a direct line to the antenna. I have crystal clear sound and have never heard any interference.
You're not using a through-glass antenna are you?