From the Super Mario Wiki
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Rob Stone is an actor and a teenage heart throb from the show Mr. Belvedere.
In The Super Mario Bros. Super Show! live-action segment "Heart Throb", Rob is being chased around by a mob of fans outside Mario Brothers Plumbing. Needing a quick get away from the crowd, Rob slips down into the Mario Bros.' home, where he seeks refuge from Mario and Luigi.
While Rob sits down to eat pizza with Mario and Luigi, he brags about his career, claiming that it isn't easy to be a teen heart throb with people chasing you everywhere and tells the Mario's that he doesn't play guitar; he simply carries one around for the image.
When Rob is able to leave due to the fact that his fans are still lingering around outside, Mario gets Rob and Luigi to exchange clothes, figuring that nobody will go after Rob if he's dressed like a plumber. Grateful for their help, Rob leaves, with his fans none the wiser.
Luigi then notices that Rob left his guitar behind and goes after Rob to give it back to him. When Luigi goes outside, he himself is then chased by the mob of people who believe that's he's actually Rob Stone.