Just making sure, but are you in true plan view, and not slightly off in
orthographic view instead, and somehow the current elevation is something
other than 0?
That's the only instance where what you pick would be off of what you want.
There is no such thing as a "fuzz" factor with osnaps - if you pick
"endpoint", and the line you are picking to is within the aperture of the
pick-box, it is supposed to go right to the closest endpoint.
If using, for example, "endpoint" on a line, do you see the "Autosnap"
marker showing up at the end of the line when you hover anywhere over the
line? Like in the screen shot attached?