offsetting your drill bit from the center of your marked location is, as I said, something less than the diameter of the finding screw on the end of the bit. Not the diameter of the bit.
The offering of up to 1/8" is valid. In all of this disussion the implication that the tenon is not too long is also valid. You are really trying for maximum shoulder contact so the joint will not wander in the long axis as the wood dries and gets smaller in cross section.