Lets just not drag this into a "black or white" argument about "every kind of map being equal to a gridlined battlemap with minis", okay? Because that simply isn't the case.
Why not?
I'm not being snarky, I just really don't see the difference.
In any game with combat you are required to come up with some method for keeping position straight. That's true of any game. There must be some method in place around the table for determining whether or not someone is where they say they are.
Now, you can do it completely mentally, or you can use minis. Either way, at the end of the day, it
shouldn't make any difference. If communication is perfect, then everyone at the table knows exactly where everything is. If someone doesn't know, they ask. If communication is less than perfect, then problems occur since people act upon false knowledge as the fireball example above illustrates.
My point is, whether you do it in your head, with a bunch of stacked dice and gummi bears, on a nice felt board with a protractor and a ruler, or on a gridded board, there should be no difference. The only thing that minis do is show the locations visually that people are already visualizing mentally anyway.
Yes, I do believe that it is exactly the same. I fail to see the difference. There's no such thing as a "rough guess" of distances. If he's within melee reach, he's within melee reach. If he's not, its ranged weapons time. End of story. The only thing that minis do is keep everyone a heck of a lot more honest and a lot more accurate.