I’m certain accommodation can be partially done without ciliary involvement, because I have done it.
A few weeks ago I had by eyes dilated for an eye exam. From my previous dilation and subsequent research, I learned the drops work by paralyzing the iris muscles. As a side effect they paralyze the ciliary muscles too. This eliminates them from accommodation.
I found on my last visit, after the drops had fully paralyzed the front of my eye, that active focus was unaffected. Same 0.5 diopter active focus as normal. But this time, for the heck of it, I also tried focusing closer than my relaxed eye distance.
To my surprise, I could accommodate about 1 diopter closer (according to the Meow-Sure app). That was proof for me that part of my near accommodation is done with a mechanism other than the ciliary muscles. And this might also explain why people who get cataract surgery sometimes have limited accommodation.
So accommodation (mine at least) is more than just ciliary muscle action. My full range appears to be 0.5 diopters beyond neutral (we call this active focus), to 1.0 diopters nearer than neutral.
My current theory is this form of accommodation drives myopia/hyperopia. Basically, the squishing and squashing of the eyeball to aid in accommodation has long term eyeball shape consequences.
Pretty cool all the ways the eyes seem to work.