Well, it is NOT an urban myth. You can become paralyze, but like wennifred said the paralysis is known as Bell's Palsy. If this does happen, which it rarely does, it's only temporary. Won't even last a week.
The short answer is yes, but it's not very common. What they're referring to is Bell's Palsy, which can happen after such a piercing gets infected. This is possible with any piercings of the cartilage in the ear.