The missing link seems to be how the police went from arriving for a noise complaint, to concluding that some of the kids were "displaying the signs of being under the influence of an alcoholic beverage." If it's just a noise complaint, there probably isn't any justification for searching the house, so any signs would have to be pretty obvious. There probably weren't vodka bottles visible on tables from the main doorway, or the parents would have noticed. Similarly, if they'd been hammered enough to be puking or stumbling all over the place, the parents probably would have noticed. The sign that seems most likely to have been noticed would be rowdiness, but rowdiness alone doesn't imply there's been drinking, especially at a celebration. It could well have been the cause of the noise complaint, but that just calls for a warning or writing-up for the noise, and letting them know to tone it down.
Just seems odd that the police would show up and notice something right away, while the parents were oblivious. A few more details from the police side could improve their credibility a lot, if it is legitimate.