[Rodney]

Don't think that's it. Snap to grid is enabled, but the major grid spacing is 1 inch and the minor grid spacing is 8, so that seems fairly "normal". (If you like to work in inches.)

I have discovered that if I repeat the steps in a new document, it behaves normally. Only this original document that I started playing with is misbehaving.

Additionally, in my original document, if I lock Layer 1, then drawing lines on Layer 2 behaves as expected. However, as soon as I unlock Layer 1, then all lines on layer 2 start at dead center on the canvas again.