I have not yet worked for a company who would class sick as being unfit for work due to drinking alchohol. Ive worked for 3 FTSE 100 companies and 3 global ones and none see it this way.
This "hes sick" is why so many companies now monitor sickness so obsessively, tracking trends, number of cases, days lost etc.
Thats also why they now regularly document return to work after sickness, potentially people can be caught lying and its deemed as misconduct.
Holiday, is days you can take off work, paid for doing your own thing. Some even offer a number of "personal days" and stuff like that, or even allow you to take a day at no notice as retrospective holiday.
When I have been involved in any sickness issue with an HR department (in management role not personally) I have found their definition to be medically unfit for work (eg a doctors definition of sick) as opposed to a general unfit for work.
Once you start accepting hangovers as "sick" how do you draw the line, whats allowed and unallowed, how many days before you get a warning, how do you handle someone who says "im not coming in today Im tired" compared to the guy who says "im sick I got a hangover cant operate machinery safely"
Generally you won't get caught out as being "sick" when you have a hangover but for a more senior member of management to tell someone to go home as "sick" when they have a hangover or have consumed alchohol would set a dangerous precedent which every other employee could then assume would apply to them as well.