This exactly. Either the deposits were insured or they weren't (as it seems in this case). Can't have it both ways, having cake and eating it too.
Ultimately, the FDIC is backed by "the full faith and credit of the United States government", which means if push comes to shove, it's backed by taxes.
Regardless of whether it really is taxes or not, it is an extra cost of doing business that the Cayman islands do not have, and therefore do not pass on to their customers. So reasonably, if one puts money in the Cayman Islands one is enjoying the benefits of looser regulation, i.e. lower costs. You can't then complain when that looser regulation includes not enforcing deposit insurance and you lose all your money.