I don't think Nintendo would make it if it wasn't safe... would they? WiFi has been here for almost a month now and nobody I know of has been experiencing any problems yet, so I see no harm in it.
It is safe, 100%, if you have encryption. And what does he mean by "not safe"? Nobody can get you viruses through a router, but they can leech off of your connection and be online too if they crack your encryption, but that's unlikely.