Nah, of course it's fake.
First you need to beat the game 3 times, then jump on the first house of GFZ1 until RedXVI goes "Blargh, who be jumpin on me tin roof?!"...
Then you say "It was I, Kernel Von Hedgehog!" and he goes "You meanie! I'ma gonna kill ya!1" and does so. You end up in Hell for being such a bad Hedgehog.
Escape from Hell if you can, being sure to avoid all the fire, brimstone, lava, and dead people, and you'll find yourself back in GFZ1, where you must pop Tingle's balloon to get a map to GFZ2, but you need to use a black shield because you can't jump that high as Sonic.
When you get to GFZ2 the map will tell you where RedXVI's house there is. It's only there as Sonic and only after you beat Ultimate mode, though. Really hard to find, too, as you can only get there by jumping from a higher platform or spindashing off the uber spring in the beginning.