There's really 3 parts to it..

1. They have no way of checking what addons/mods one has installed, and because there are ones they definitely do not want to be there they're just making a blanket statement that all of them are prohibited.

2. The only way to use them is to actually modify the game itself and they don't want people doing that, and also against the ToS.

And a slightly lesser third, Yoshi did say that they're not gonna be responsible if anything happens to your PC or your account from someone possibly hiding some malware in the tools, mods or addons...