Reading the B737 Classic FCTM it says "The airplane can land using crab only (zero sideslip) up to the crosswind limit guideline speeds. On dry runways upon touch down the airplane tracks toward the upwind edge of the runway while de-crabbing to align with the runway."
To me that implies you can safely touch down sideways without removing drift.
Perhaps Boeing should have added with a sly wink "And the Devil take the hindmost." To those who have seen this happening and shuddered at the thought, remember the old adage "Neat but not gaudy - like an elephant's arse sown up with a bicycle chain," might humour the frightened.