Our company has a strong mission and values statement that we follow- not just lip service. HR’s role is to support the mission and values, uphold the law, and assess what is the “next right thing” for the employees AND the company. If we make a mistake with respect to an employee, we do what we can to correct it. Our HR department works closely with me every single day to make sure the correct decisions are made and that every matter is investigated thoroughly. I know I am fortunate and that every company isn’t like that, but I could not work for a company that disrespected its employees and/or acted inappropriately.
We are all coming at this from our own perspectives, of course (with respect to the OP’s dilemma) and I can understand the different viewpoints. Perhaps a conversation with the alleged drinker himself might be the place to start. Uncomfortable, but maybe necessary.