A bet is a bet. Even a mini-bet means something a check doesn't. The fact that the player bet the minimum rather than checking means something. This distinction between checking and mini-betting is more important than Miller seems to be saying here. There's no benefit in deliberately conflating small bets with checks - if anything, this smacks of the sort of mental laziness Miller is railing at.
I often make a min size raise online because I was not paying attention and the time is ticking and I want to make a raise but don't want to fool around and risk a time out.
I agree that any attempt to lump all small raises into some standard category is pretty much just intellectual laziness.
The important thing to keep in mind is that in multi-way games (even if the action has gotten to heads up) you're going to have to do things that are unexpected and contrary to the norm to get the money. That's what strategic thinking is all about. It's important to consider the possible reasons for the min raise, and Random Shuffle is right that there's always a reason and the reason is seldom intellectual laziness. Other than the being in a hurry reason, the two main reasons are as an attempt to seem weak and entice a raise and an attempt to take away the initiative while keeping the pot small.
A player who is making the min raise for the first reason is hoping you'll think it's for the second reason.
One of the holes in Miller's thinking is a common 2+2 shortcoming, a failure to recognize that even when your opponent is making a mistake he often thinks he has a good reason to do what he did.