If it blew when the TV was off, it sounds like a short, not excessive power draw. Check the TV back for it's rated watts and amps. If it's within the 15 amp range, then the service center is not dealing with the real issue. It's always unwise to just increase the size of the fuse, overheated wires or a fire could result.
You could also check the manufacturer of the RV to make sure of the size of the fuse.
Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI