An internal combustion engine works by combining fuel (gasoline) with oxygen (from the air) and adding a spark to make it go kablooey. There is an ideal mix where you balance out the oxygen and the fuel so that you get the biggest bang inside the engine. If you have less fuel than this ideal mix then your engine runs lean, which means all of your fuel is used up and there is extra oxygen in the mix that isn’t doing anything. Too much fuel and the engine runs rich, and all of the fuel doesn’t burn. Balance it out just right and all of your oxygen and all of your fuel is used up and you get the best engine performance.
To make a more powerful engine, you need it to burn more fuel and oxygen. Adding more fuel is easy enough, but your air has a limitation. The amount of air that your engine can suck in depends on the air pressure.
This is where the supercharger comes in. By ramming the air into the engine, the supercharger allows more air into the combustion chamber, which means that you can put more fuel in (again, trying to maintain that ideal mix), and you get a bigger bang, which means more power. Or your engine just explodes if you didn’t design it to handle the bigger bang. But assuming you designed your engine to handle it, you get more power.
If your engine is running properly, then adding fuel into the supercharger is going to screw up the air/fuel mixture, and it’s also going to mean that there’s less air going into the supercharger (the fuel will displace some of the air). So your friend is right. It’s going to make the engine run rich and will make the performance worse, not better.
However, notice that I said “if your engine is running properly”. If the engine’s fuel/air mixture is screwed up because it’s not tuned properly or the fuel filter is all clogged up or some other reason, then the engine will be running lean and adding fuel will get it closer to that ideal mixture and it will run better. So you can technically get a boost, but it requires your engine to be kinda screwed up for it to happen.
Personally, I’d rate the idiot hanging from the front of the vehicle playing the guitar, the goofy pole acrobatics, the title character doing very little (this was more of a movie about Furiosa than Max), hugely underdeveloped characters throughout, and the piss-poor plot as worse than the fuel spitting idiocy. But that’s just my opinion.
So I agree with your friend on two points. First, the fuel spitting wouldn’t work, and second, it was a stupid movie.