Cool video! I will show them to prove that they are mega babies.
Keep in mind that the reason why they might feel that Project M is less responsive than Brawl, despite having less input lag, is because Brawl will buffer your next action with 10 frames and will execute it as soon as possible. You can see how this works in this video:
https://www.youtube.com/watch?v=DYFnneqyMbw
At the start Falco jabs, but the player hits B within 10 frames of the jab being executed, before the animation is even finished, then the laser is fired as soon as the jab is completed without any additional input. You can see that the player completely takes his thumb off of the buttons but the laser fires anyways. This does not occur in Melee or Project M, you must wait the for the jab to complete before the game will register the input for the laser. Second example shows Marth short hopping and the play double tapping the C-stick forward. Marth executes a forward air and then a forward smash once he touches the ground without any additional input. Again, this does not work in Melee/Project M. This allows less technical players to be less precise with their inputs, but it can also cause a lot of unwanted actions during complicated and technical maneuvers for more competitive players. After playing Melee for a long time, the 10 buffer frames makes the game feel very sloppy, loose and imprecise. The Input Assist option is meant to ease Brawl players into the Melee/Project M way with a stricter 3 buffer frames, which is still a bit more lenient than the default 0 buffer frames.
I doubt this will change the minds of your friends, even if they understand the differences they'll still most likely point to the Brawl system and say they like it better since it's what they're used to.