Please forgive my mistake.
The fault here, was that I use "ZeroClipboard" - https://github.com/zeroclipboard/zeroclipboard
Though I'm not actually using it explicitly on this page AT ALL.
But somehow the kendo editor teases it into showing/appearing... and it for some reason creates an invisible barrier to which clicking cannot penetrate.
The reason it didn't happen in Firefox, for me, is because I don't have flash installed for Firefox.
I hope this helps somebody else, if nothing else.
Meanwhile I'll need to find out what is wrong with ZeroClipboard to do this.