I believe you are correct.
PS. You should listen to Keith on this subject. When I said that I thought you were correct in thinking that the material determined the grade of the bolt, I was including the material processing as part of the "material". So a heat treated piece of steel is not the same "material" as an annealed piece of the same type of steel. The tie-in to the "material" is not so clear when it comes to other types of processing. A machined thread does not have the same strength as a rolled thread in the same material.
Hi Alexander. Sorry - this is going to sound a bit overbearing, but if you're assuming that the material has a determining factor in the grade of the bolt, you're in the wrong business or maybe you're a student. The grade of the bolt is governed by the material and that material's heat treatment and finish. A 'Grade 8' bolt can have many sub-grades; for example a Grade 8.8 bolt is made from steel that has a nominal theoretical ultimate tensile strength of 800MPa and a theoretical yield strength of 0.8 x 800MPa (i.e. 640MPa). The actual strength of a bolt-and-nut combination is determined by many factors (insertion length, thread quality, thread form, etc). So be careful - the Design Library gives you a MODEL of a bolt, not a bolt that you can use to obtain mechanical properties of a bolted joint, etc.
All the best, Keith