I love logic so ill be the devil's advocate:
The United States law (its actually state law which dictates 21 as the year, but whatever) recognizes that time can be measured in different intervals. Technically, you could count down to an infinitesimally small unit of time to measure your age. They could have measured it by the month, so in February you could have purchased a drink. They could have measured it by the hour, so you might have to wait until 4 to purchase that drink. They could have measured it to the minute so you would have to wait until 4:10. They could have measured it to the second so you would have to wait until 4:10:XX. But they didnt. They decided to go with the DATE of birth, not hour or minute of birth.
Its not an edge treated with leniency. An edge treated with leniency would be like purchasing your first drink on 10:00pm the night before your birthday. In this situation, the cutoff point was when the clock strikes 12, not because it was the actual time of birth, but because state legislature recognized it was the easiest and simplest way to keep track of age. The laws are written with a 24 hour window in mind. If youre in that window, you qualify to state that day as your Date of Birth for purchasing alcohol, even if you are at the extremes of both ends.
Slipperly slopes are a informal logical fallacy, not a formal one. Formal logical fallacies are fallacious by nature, and should not be used to argue a point. But keep in mind that violating the fallacies doesnt always mean its false.
Take the classic example of a formal logical fallacy: If its raining outside, I will get wet. I got wet. So it must be raining. This is a fallacious argument since there might be other causes of getting wet. Does that mean its not raining? Not necessarily. It could be raining, which is why i got wet. But it could have been from another source of water as well, so the logic is false whether or not your conclusion is true.
Informal Logical Fallacies are fallacious, but not due to logic. They are fallacious by relying on human tendencies and generalizations. Again, this doesnt mean they arent true or dont describe the world correctly. its an informal logical fallacy because its something to keep you suspicious of the argument, not outright denying it. (Outright denying Informal Logical Fallacies is a fallacy in itself, BTW). Informal Logical Fallacies require more insight to determine truth than formal logical fallacies, since nothing about the claim is inherently false.
For example, take this argument - The sun rose every day for the past million years, so the sun will rise again tomorrow. Thats an informal logical fallacy. Is it false? I dont know (and nobody can). But would you bet that I'm going to be wrong? Informal logical fallacies are everywhere, and cannot be avoided. Whether you recognize it or not, you rely on informally fallacious reasoning every single day.
Similarly slipperly slope arguments arent always wrong, I wont give an example, since it would make this post about 3 times as long, but there are instances in Law where it occurred. If you want one, ask and i shall give.
Letter of the Law vs Spirit of the Law is an interesting debate. For better or for worse, generally the Letter of the Law wins, because one of the main focuses of written law is having the ability to read the law if you so desire. If the laws were not codified by statue, you would never know when a law changes. Unfortunately, the Letter of the Law isnt always clear, coherent, or legal (due to many factors, primarily that Legislatures dont know the law, dont account for how its interpreted, or that laws go through dozens of amendments before being codified, so the final product doesnt look anything like the original). Then the courts can go to the "spirit" of the law, evidenced by congressional debates and briefs, as long as it isnt blatantly in conflict with the letter of the law.
this is my roundabout way of saying that in this case, the Letter of the Law states that anything past the scheduled time is late, but you get a 10 minute grace period. We can argue about what the Spirit of the Law is (and only the person/people who wrote the rule will know) - is it to discourage "dozing off" opposed to "setting up camp"? (i dont understand that metaphor). Or is it to discourage being late in any way shape or form, but knowing that an absolute no-tardy rule would be too absurd? What happens if 2 people wrote the rule, one thinking that it was to discourage "setting up camp" and the other thinking it was a no-show rule?
EDIT - my bad, i didnt read your post thoroughly enough. I get your letter vs spirit metaphor now. I would say that neither are in violation of the law. The law prohibits sleeping, so the one setting up camp isnt sleeping, and therefore, isnt in violation of any law. The other, who is dozing off, isnt not in the proper mindset that his consciousness is lost to be "sleeping".
And secondly about your point with Juveniles, there IS a hard cutoff. Most states have a codified rule with the exception at 16 (some at 13, some that have another exception for murder). Juveniles under 18 are charged as Juveniles with more lenient sentencing, but the system codified a 2 year buffer for serious crimes. This situation is similar with, with the rule at 3:00 but with a 10 minute buffer. In the states where a 16 year old may be charged as an adult, a 15-and-11-month cannot.
