Well, half right, I think; two more variables should be considered: how the rod bends (the action) and the fisherman himself.
Two persons may push a rod in two different ways; one finds the rod O.K. The other one, a more robust caster, thinks it is too weak. His force can´t be caught up by the rod; he "pushes through" the rods action (optimal bending curve). So he breaks the backbone of the rod.
If the same rod could have another action (utilizing a steeper progression), or the rod made shorter or made for a heavier line, he might have approved...
Generally speaking there is a harmony between rod length and line weight. This is a sound fact to start from, but very decisive factors are the action and who is using it. However, there are many a rod constructed for the most "odd" line weights that perform splendidly, say eight footers for # 3 lines - or # 8 lines ...!
To achieve this it´s always a question of using the appropriate action.
What line weight?
A good rod responds well to two line weights or more; if it is an 8-footer or longer probably three or four different line weights could be cast without a wavering line or the rod being overloaded. But you will certainly favor one weight over the other as that weight brings out the action in a way that suits you.
Maybe you even favor one brand over the other, both line weights the same. It´s quite normal.