Since I am usually the guy just learning, often times when I roll in an open class you start doing the drills like you said, but I talk with my partner (who is usually more skilled than I am) and after we go over postitional stuff guard to half guard and whatever techniques they are trying to stuff in my thick head....I generally say, ok lets go for it and increase the resistance.
This is done gradually, it doesn't do me any good if the guy is bigger and badder than me to keep tapping without me knowing what's going on and trying to learn to defend.
So, usually my partner will allow me some postional change...if he is in guard, and I am trying to basic a choke without setting it up and allowing for him to pull me into a triangle, well the understanding is that he pulls me down hard enough to let me know he could go for it, but explains my mistakes.
Then we do it again and again and again, but eventually he won't be so gentle and I won't be so stupid. In this way, you increase intensity continually but gradually, with the understanding that we aren't trying to clobber each other (or at least I won't get clobbered)...so I can learn.
If I get out of something he is trying to pull on me, I know I did it and it wasn't him releasing me. Otherwise you might question how you escaped, if the intensisty isn't there.
The biggest problem I had to get over was being too aggressive, to my detriment. I got tapped quickly, but learned little.
So intensity...but with communication and an understanding of how "hard" we are going to take it.