No they dont own it...but they will attempt to police it.
The RIAA is already preparing itself to retrospectively sue everyone that has broadcasted anything, ever. The further out into space our radio leakage gets the larger the number of possible extraterrestrials there are to sue.
I for one cant wait for the massive influx of tax from UK TV licensing. We've been broadcasting for decades thats a lot of free TV the aliens have had...its an outrage. On the flipside they will have trouble when the digital switchover happens for them...