All published information is in the public domain unless a specific, copyright exemption temporarily applies to withhold it.

You sure about that? In the US, the creator of a work has automatic copyright over it, whether it's published or not: https://www.copyright.gov/help/faq/faq-general.html

If you meant something else, or there's a modifier to your claim here that I'm not seeing, maybe you could clarify?

As with most legal matters, it depends: https://www.copyright.gov/fair-use/index.html

Purpose and character of the use, including whether the use is of a commercial nature or is for nonprofit educational purposes: Courts look at how the party claiming fair use is using the copyrighted work, and are more likely to find that nonprofit educational and noncommercial uses are fair. This does not mean, however, that all nonprofit education and noncommercial uses are fair and all commercial uses are not fair; instead, courts will balance the purpose and character of the use against the other factors below. Additionally, “transformative” uses are more likely to be considered fair. Transformative uses are those that add something new, with a further purpose or different character, and do not substitute for the original use of the work. Nature of the copyrighted work: This factor analyzes the degree to which the work that was used relates to copyright’s purpose of encouraging creative expression. Thus, using a more creative or imaginative work (such as a novel, movie, or song) is less likely to support a claim of a fair use than using a factual work (such as a technical article or news item). In addition, use of an unpublished work is less likely to be considered fair.

I don't know many schools willing to bother finding out whether the use was fair.

We're actually discussing educational purposes and fair use in this thread:

https://lemmy.world/comment/7787391

So far, the consensus is "probably"