Unity Car Tutorial (alt physics) building for web incorrectly.

Whenever I load the Unity Car alternate physics tutorial in the editor, everything shows up fine, and the car runs exactly how it should. However, when I build for web, it seems that all of the well set controls fly right out the window and the car starts doing whatever the hell it wants: the wheels don't spin (but you do drift forward somehow) and the wheels don't turn - you somehow turn the opposite of the direction you want to turn.

This is all directly out of the box on a fresh install of unity, no settings changed.

Is this some kind of known bug? Where have I gone wrong? (This has repercussions for my actual project beyond the demo, being based around this physics model.)