If the piston is flush or below surface of caliper housing, you are correct. Either rotor is too thick or pads too think. Can't imagine them making a mistake after selling so many kits. It will boil down to their supplier (if it's not you)
You are using the correct approach, trying to fit the rotor into pads without mounting either. I assume all pads are the same thickness and not one thicker than the other.
I assume they will measure the pad thickness of another set and tell you the dimension for you to check yours. As you know the fit is going to be tight. That is normal for disc brakes.
We have all had this trouble when we replace pads. It's always been that piston needed more squeeze.
