The question says if (1) y = kx + b is parallel to (2) x = b + ky, what is true about k?

The answer explains that equation (2) can be rearranged to from y = x/k - b/k.

For the lines to be parallel, the slopes must be equal, so k = 1/k, k*k = 1, and k = +1 or -1.

HOWEVER, I understand that two parallel lines must not share any points, i.e. not be coincident. Thus b must NOT equal -b/k; hence k must NOT equal -1.

Thus for the lines to be parallel (same slope and yet distinct lines) k = +1 only. The answer should be B { k=1 }, and not D { |k|-1=0 }.

I am going by the definition that parallel lines never meet. Is this correct for the GMAT?