In the grand scheme of things, this kind of semantics is pretty for down the “needs” pyramid, but I will throw my 2 cents in.
Because of the Hanoverian naming convention, with the horse taking the first letter of the sire’s name, “G line” most definitely implies the horses’ sire line. If I were commenting on my TB-Hanoverian mare, I would state that she is by Wilawander out of a G line mare. I mean, if you don’t follow this convention…where would you stop? The 2nd dam may be Rubinstein. So…you wouldn’t say the mare is an “R line”, would you?
The sire line, is the sire line. And this is exactly why the HV has started stamm numbers just like the Holsteiners.
So it would be more accurate to say x horse comes from, or carries “G-Line origins” if I follow your logic? Than only x horse is a “G-Line” horse.
In french I would always say: x horse “descend de la lignée G hanovrienne” wich does not mean “IS A” but more like “comes FROM” So would that be better?