Well that is not totally true, he commands her quite a bit during sex and the wine bottle scene is all MC, Lacey just told him it was ok to do it.
He also requests the "special nights" in act 2.
What is true is that we never see MC initiate aside from 2 times after the lorenzo incident (1 in each path), not even with the other LIs.
Punish:
MC "I can respect that."
MC "If there's anything I can do, let me know."
L "I will."
MC "Now. None of this changes that you did cause havoc tonight."
L "I really did, didn't I?"
MC "I wish I could look the other way when you do things like this."
MC "But what would Anna and Mia think if I let you get away with it."
L "You're right."
MC "Are you sorry Lacey?"
L "I'm very, very sorry."
MC "My dick doesn't think you're sorry."
MC "You should apologize to him."
MC "And be quick about it."
Slut:
MC "I can respect that."
MC "If there's anything I can do, let me know."
L "I will."
"I stop a moment and take a deep breath."
"I'm way out of my comfort zone with what I'm about to do."
"I hope she understands it's just a game."
"Please let this go well."
MC "You said you wish you weren't some dumb slut."
MC "But, isn't that what you are?"
MC "You're just a dumb slut."
MC "You know that right?"
L "Wh...what?"
MC "You can't keep pretending that the girl you were in college wasn't you."
MC "It was you."
MC "You did all those things."
MC "And that makes you a slut. Right?"
So I don't think we have a leg to stand on with this theory, it is just how the author writes.
What the slut dialogue made me go and look for, is this:
L "It obviously happened."
L "I obviously had way too much K."
L "
I guess I was some kind of raging slut again."
L "I never wanted to be her again."
L "But maybe there's a part of me that's still that girl buried somewhere inside of me."
L "So far down that only being insanely high makes it come to the surface."
L "I don't know how else to explain any of that stuff I said."
L "I certainly don't actively think those things."
All the talk about self punish kind of went out the window, I mean not entirely, but I now have difficulties to match many of the dialogues Lacey has about her past when faced with this admission.
Another interesting we can extract here is that the other side is not her being a slut, since she is aware of the other side but unaware of the (not real) raging slut.
edit
Well we don't know anything about that, but we know that Barty has a horse dick, like 99% of the men present in the game:
MC "Really not sure. Something about your dick."
BA "HAHAHAHA you must have talked with my wife."
BA "She used to call me big guy."
CrysusPariah2 Going through the dialogue with drunk Barty makes me think that the barty visit to lacey for the video has to be placed before his drunk visit:
BA "I want your wife to do it."
BA "She's good at it."
show barty_drunk at midright with move
BA "She's such a great..."
BA "such a great little slut."
BA "You're so lucky."
MC "Barty, you need to tell me what the fuck you're talking about."
BA "And plus... and plus..."
show barty_drunk at right with move
BA "She swallows."
BA "I know right?"
MC "I'm going to ask you one more time."
MC "What the FUCK are you talking about?"
BA "Shhhhh, keep... keep it down."
BA "Her husband... Lacey's husband, he can't find out okay."
BA "He's not supposed to... (hic) know about it."
I mean half the things he says are things that can be reconciled with the video so...
I know he is supposed to have found some Llacey's online presence but it seems glaring, maybe I am reading too much into it.