The dodgyness ("caninety?") in this case may actually be a result of their non-dodginess ("felinity?"):
Estonia is big on e-government and have apparently made the process of registering an llc really easy. That attracts all sorts of people for whom it makes a difference if the process costs $100 or $110. And that is – as a group – self-selecting for people you can't necessarily trust as much as others. The same mechanism is at work with British LLCs. Those became somewhat famous (being first in this market) because they were often used by people who couldn't start a company in their native country – most often because of messy bankruptcies that can get barred from trying again for certain periods.