We use the principle of what my original teacher termed Kinesthetic Invisibility, where there is no real perceptable physical reference to react against. This goes a long way in "allowing uke to unbalance themselves" - yes, with a little help, but if done right it doesn't take much, and isn't about doing something To them.
Perhaps this is a logical distinction, but I feel that the intention of uke and nage need to be taken into account when discussing things like this. Of course well done kuzushi doesn't take much, that's how kuzushi works, but the question in my mind is whose version of the desired outcome is actualized? If uke's goal is to grab or stike nage, they have no intention to be thrown or thwarted. Nage's goal is to avoid injury and throw or otherwise disable uke's goal of harm. I don't care one bit how 'easy' or subtle nage's movements are to off balance uke. Even if they're using uke's own reflex arcs against them, their (nage's) intention is causing uke's loss of balance and nage has to face the fact that they went into the encounter with ego and intention and that there's nothing wrong with that. Yes the strategies can include moving as a unified whole (moving with uke as you say), and some of the really subtle stuff may occur almost exclusively within nage's body, but the intention of the encounter is that of nage imposing their will over uke. I simply refuse to believe otherwise, it makes no logical sense to me, and I have never felt it from anyone (including a lot of people claiming that was what they were doing). So if you're adding that little bit of help, why not admit the reality of the encounter and accept your role in the encounter? (Please read that last sentence as a rhetorical question, and not a direct attack on you personally.)