Wozza, your rear QR is 4mm or so, not 9mm.
The axle diameter/slot in the drop out is 9mm on the front, 10mm on the rear. The rear 10mm is the most common mentioned but the front equivalent is 9mm.
OP – yes, the 9mm QR should fit in a normal QR dropout. The hub omits the 9mm axle bits that sit in the drop out and yes the thinking is the larger axle is less stretchy. Problem is you are comparing a 4mm or so bit of steel to some aluminium so there needs to be 3x the cross sectional area to get the same stiffness in pure tension. I think an additional benefit comes from a larger diameter where the end fitting are as there can be some flex in the nut/cam at the end when the forks are flexed. But remember a shimano internal cam QR is a very god design and can get some pretty high tensions.
Proper through axle takes the same philosophy but just goes bigger so has stiffness and weight benefits.