If you have a lock screen password/code etc. then you first have to connect your iPhone to the iTunes on your computer. The two will then perform a handshake where you will unlock you phone and say Yes to a notification on your phone asking you whether or not to trust this computer.
As far as I'm aware, the issue that you were having is that Image Capture does not perform this required handshake, so the phone doesn't know to trust this computer until you connect it through iTunes. PS. You should only need to do this once, after that it should work without iTunes, but don't quote me on that.
As to why iExplore worked, I'm just guessing, but they've been known for finding really cool loop holes in iOS for years, so I wouldn't be surprised if this is just another sweet trick they found. Or most likely they just do the an iTunes-like handshake. ;)