My interpretation of this is the similar to the food policy for the parks. On the website it clearly states no outside food or beverages. In reality, they have no problem allowing snacks, water, etc to be brought into the parks. What they don't want is people bringing in a full cooler of sandwich items, laying it out on a table and assembling their lunch (that is why you can bring in a whole sandwich, but not the individual fixings). They ask that if you want to do that, please use the picnic area.
The same goes for the alcohol policy on DCL. They are fine with you bringing on your own alcohol as long as you drink it in your room or one at time while out on deck. What they don't want is people bringing full coolers of bottles up on deck and handing them out around the pool, etc. It was stated before that they had problems with coolers in the rooms leaking and making a mess of the carpets, etc. But I can also see where they wouldn't want coolers of bottled beer or wine around the pool either.
But because they can't be that specific on the website, they include the wording as they have. Mainly because if you don't have something in writing people will take it to the extreme
(give them an inch and they will take a mile) and then they will have to ban bringing on your own alcohol completely.
They aren't going to stop and check each cup to see if there is alcohol in it, but if you show up at the pool with enough alcohol for 10 people for the day, they might ask you to return it to your room (and can state the policy as the reason why).