There are no speakers anywhere near it, except for the ones installed in the TV.
I'm nearly 100% sure it's a problem with the TV itself, and not an interference of some kind.
I've decided to take it back and exchange it. The only thing I worry about is whether the replacement will have the moire too. With the way TVs are made today it could be a problem with this particular model line. I tried checking out the display models at the store but they're sitting high on the shelves and I can't see the screen good enough.