So, specifically with Prenda, those copyright assignments presented in court were forged. Shell companies listed on those documents were also concocted with forged signatures. Should an ISP be expected to investigate claimed copyright assignment, including shell companies; or should Prenda prove that small civil stuff like this needs strong legitimacy or it will attract fraud?

What do you think the ISPs needed to know? If they had done a comprehensive investigation, it would have shown that Prenda was fully authorized to act on behalf of the copyrights they asserted.

Prenda wanted to conceal from the court that they were the copyright owners and not just hired agents. But that isn't a question of the legitimacy of the copyright assignment. Being threatened by the copyright owner isn't less legitimate than being threatened by a hired agent!