What value do you put on integration tests?

During my one on one with my boss, my boss mentioned that most of engineering does not use our local development environments for testing their work.  He continued to explain that most engineers are relying on GitHub integration tests to test their work.   Quite understandable as our local environment does not support many of the behaviors of our system, nor make it easy to test parts of the system.   It's a difficult environment to work in, locally anyways.

However I am still at loss for words.  Especially given that I have demonstrated our integration testing is poorly done.

What do you think?  Can engineers avoid manual test through use of integration tests?

I would like to hear your thoughts.