If we're going for diagnosis-via-internet I think that it sounds a lot more like ILD (Intermittent Lawsuit Disorder). It's a pretty classic case - sudden displays of aggressive legal threats, weirdly self-righteous justifications, conflating criminal & civil law, completely disproportionate responses, and assertion of bizarre offenses. I think it meets most of the criteria in the C&DSM IV.

Less flippantly I think that there may be a pretty strong correlation between these behaviors and personality disorders, but bullying and animal threat display behaviors are still relevant models. It's potentially a big mistake to confuse one of these people who is panicking and trying to use intimidation as a response with someone who has slipped into a state of irrational anger & obsession. The former can be dissuaded or possibly negotiated with, the latter is more likely to just keep escalating. In particular I'd presume that the latter are more likely to actually file the frivolous lawsuits and it's a higher priority to get everything locked down on the legal front. Generally a good idea anyway.

The idea behind requiring quick action on someone's part is to exploit the emotional impact of a demand so the person who is being backed into a corner doesn't have time to think and just reacts to remove the pain.

Without a time constraint people end up gathering information, and getting over the psychological shock that clouds judgement.

A somewhat similar concept (not related to this) is the idea that "time kills all deals". The more time goes on the less likely a deal will occur.