Was once involved in a road accident and was questioned in that manner, my "Life experience" wasn't good enough...My admission that I couldn't smell his breath due to the petrol fumes around the scene nullified my evidance, and his behavious migth have been due to the trauma of the accident ? Yeah ! Right !
You'd better be sure the Company are behind you before you deny boarding, commonsense has nothing to do with it, The Law Is An Ass.
Whilst this may be true of a post event argument over who was right and who was wrong, in a pre-event boarding of an aircraft the captain can say he doesn't want that person on board for whatever reason, and the law will be 100% on their side. The airline can then look to rebook on another flight, either when the person has sobered up or had time to explain their behaviour, but there will be no legal come back for not being allowed to fly.