As I read it, the vagueness referred to is not in the rules, but in their application in actual play - that is, without a grid it is not clear who is within 5', or 10', or whatever, of whom. Similarly, I think this is why the reviewer thinks that the cover rules create "more room for arguing". The arguments that are anticipated are arguments about who is how far from what.
This.
It happened in our Starter Set session. I told players to ignore the square grid and put their PCs where they wanted them to go. Since miniatures were all over the place, there were a few times where it was difficult to tell if a close miniature was actually an adjacent miniature.
In theater of the mind, this would be a nightmare for my group (especially between my wife and myself who can misinterpret each other merely from tone of voice
