I would guess you are both correct, but the word "line" is rather ambiguous.
As is evidenced in these 2 posts, it can refer to everything descended from the original morph, or it could also refer to a much smaller subset.
The best example of this that I know of is in corn snakes. Abbott's okeetees are very well known, and I don't think anyone would dispute that they deserve to be considered a separate line. However, I've heard that most if not all of Lee Abbott's founding stock was selected from the Love line of okeetees. Okeetee itself is just a line of normals that came from a region that tended to have more brightly colored snakes. So that's 3 different lines (of normals!) that all originated from the same group of WCs.
I have also wondered about how they know if any one particular woma carries the hidden gene. Even if it descended from the hidden gene line, that doesn't guarantee it has the gene. There must be subtle visible differences, but so far I've never heard what those are.