I think everyone agrees that the hip extension needs to be fast and complete. The "muted hip function" you are talking about is simply a failure to extend the hip joint. The question here is whether or not the hips should travel forward, into the bar, during this extension and what causes that forward movement.
I think it's a matter of timing and coordination of joint movement. Let's assume the knees have already rebent and the bar is approaching the top of the second pull. That's around mid-thigh in the clean, aka The Jump Position. In order to push the bar forward with the thighs, the knees must extend such that the knees are a pivot point. In other words, the knees are kept from traveling back towards the lifter. This will cause the thighs and hips to come forward into the bar.
Here is the important concept: Hip extension does not cause the thighs to hit the bar! Pure hip extension causes the legs to move back and the back to move back, relative to the hips. Nothing is moving forward, if all other joints stay the same. It is knee extension that moves the hips forward into the bar!
So what error of timing can cause the thighs to bang into the bar? Well, one error could be a delayed or muted ankle extension. From a ready-jump position, if the knees extend but the ankle angle stays the same, the thighs will move forward into the bar. If the ankle extends at the same time as the knees extend however, the knees will move BACK, taking the thighs with them. The bar will not hit the thighs.
In the Romanian Deadlift as I have been taught, the knees are slightly unlocked but do not move. With no changes in knee angle, there is little-to-no quad action. The butt moves back by extending the ankles and flexing the hips.