Brake Light problems of the 2010 Volkswagen Jetta Sportwagen

Electrical lighting monitoring system started going through several actions indicating right front low beam was out, then left rear brake light was out, then front, right signal light was out, then left rear signal light was out, then license bracket light was out. All this happened while the auto was being driven on a straight section of highway. Carried auto to local service man who said it would be better for Volkswagen to look at it, as it involved major electrical problems. Although car had been turned off, the battery had to be re-charged to get the car to start in order to carry to dealer - 45 miles away. Was told by vw dealership that it sounded like the fuse box had melted. Stated they had seen several incidents of this. Actual diagnosis was the fuse box had melted. I commented that this seemed strange. I thought the purpose of a fuse box was a safeguard to prevent overheating and that fuses were suppose to blow and stop the current flow if there were problems in the electrical system.