The coconut crab is a very popular delicacy in Batanes. I requested Fundacion Pacita to get one for my dinner for i want to try it. ;-)
The species is popularly associated with the coconut, and has been widely reported to climb trees to pick coconuts, which it then opens to eat the flesh. While coconut crabs can climb trees, and can eventually open a coconut collectively, coconuts are not a significant part of their diet.