If your real-life friend's PC is going to die and you are the DM of a game without minis, do you really want to deprive him of the potion that would save his life? Do you really want to be seen as a jerk, when all you have to do is say, "Yeh, you manage to get there in time"?
HOWEVER....if there are minis on the table and they are far apart, what can a DM do? His hands are tied, and nobody thinks he's being mean for letting the PC of his friend bleed to death.
What I'm saying is, If you are a friendly DM, you will help the PCs during battles whenever there is a crisis. And if you are a wicked DM, you will nudge events to hurt PCs whever you can. Players will eventually pick-up on your patterns, and your game will be more predictable (at least more predictable than it would be were it using minis).
If a mini-less DM asserts his desires and emotions do not come into play during battles, he is either mistaken or he is as impassive as Spock. Or he is a stranger at a convention who doesn't care if he sees you again.
Tony M