I had a similar issue where after an upgrade my insync broke on Ubuntu MATE 16.04 LTS. In the course of troubleshooting I did check my apt sources and found what @lpugoy said about the source for insync being set to trusty instead of xenial. Manually changing the source file fixed it no problems after a sudo apt update && sudo apt upgrade
For what it's worth to the insync folks, I installed mine via the built in Ubuntu MATE Software Boutique. I don't know if that is similar with others who saw this issue or not, or if that helps with tracking down the source of the bug.