This seems to mean that "No one 17 and under admitted." isn't phrased very well?
It's inaccurate to construe it in a sense that it conveys a legal obligation or prohibition that is inherent in the rating, and thus that the rating agency has legal authority to enforce access restrictions for minors. The MPA can advise that the film is unsuitable for minors and may state the reasons for its determination. But whether a theater actually forbids minors to see the film is largely a matter of the theater's policy.
However, as you approach the NC-17 content you approach material that is considered by statute to be harmful to minors. It is criminally unlawful in almost all jurisdictions, for example, to exhibit explicit sexual content to a minor. It is the nature of the material itself, not some third party's opinion of its suitability, that determines criminal liability. A theater could exhibit an unrated film that has explicit sexual content, and would be criminally liable if it did so for minors. It is perfectly lawful to exhibit an unrated film to the public, but it is not lawful to exhibit explicit sexual conduct to a minor regardless of any third-party rating.
The NC-17 rating can fairly put cinemas on notice that they should know the material is unsuitable for minors in the statutory sense. That's where it finally has some teeth. But it's still not a legal requirement to have an MPA rating before you exhibit a film. Nor is the MPA's opinion of the film's content of any legal significance in determining whether a minor has been harmed.
Further, there are lesser offenses such as contributing to the delinquency of a minor that might come into play for lesser film ratings like R or PG-13. Here again there is literally no legally enforceable obligation to keep children under 13 from viewing a PG-13 movie. But because the rating puts a theater on notice for the content, it can be considered fair warning of the delinquencifying content. But in all such cases at law, it is the nature of the content as determined separately by the court that matters, not the rating.
But you have to be careful, because civil claims for contributing to delinquency can arise if a theater ignores a
policy they might have of respecting the age recommendations in the MPA ratings. If a theater has a policy of actually requiring proof of age for PG-13 movies, and it lets in an unaccompanied 12-year-old without proof of age, then there may be standing for the parent to sue. But I wouldn't take those odds.