I think it's the effect of "bastard" which is what makes it especially poiniant to English speakers. It's a bit stronger than "troublesome people."

My Latin dictionary doesn't have an entry for a form of illigitimi, but it does for nothus (3): bastard; counterfeit. I also can't find anything for corborundum, but it does have an entry for "grind down", opprimo (3), and "grind", contero (3). But, my dictionary isn't a large one. I need to invest in a comprehensive Latin dictionary and Medieval Latin dictionary.

One thing, of course, is that Latin mottos often don't make any sense when translated literally into English. There's often a bit of freedom exercized.

Cheers,
Nick