The transfer system that exists for 3->4 and 4->5 did not let you send a Pokemon forward if one of its moves was an HM move. Unlike Defog, which was safe to go via HGSS (because the HM restriction didn't apply to ordinary trades within the same generation, and because they changed HM5 to Whirlpool instead of Defog), Surf was an HM in all games, so there was no getting around the fact that if you wanted to send it forward, you had to delete Surf. Relearn moves were not a thing until 6, so deleting Surf from those games meant deleting any indication that it ever had Surf to begin with, and once you do so you can never get the move back. Thus Surf + Nasty Plot is actually incapable of coexisting, and the sim is properly recognizing as much.
Note that if you try to validate a Pichu with Surf (but not Nasty Plot, since that move didn't exist yet) against Gen 3 OU, it shows up as legal, proving that Showdown acknowledges the existence of that event, but if you try to validate against Gen 4 OU, it's illegal, which likewise proves that it knows about the inability to send HM moves forward. Normally this isn't an issue since you'd be able to simply re-teach the HM in the newer game if you really wanted it, but the whole Surfing Chu premise is anything but normal.