Under the theory in these suits, wouldn't Half-Priced Books have to actually vet their inventory to ensure they only sell books that have undergone a proper domestic first sale authorized by the publisher? It doesn't seem to be enough that Half-Priced Books themselves refrains from engaging in a parallel-import scheme. The strong version of the argument, at least, seems to be arguing that the first-sale doctrine doesn't apply at all to books that were imported without the publisher's consent. So not only would parallel importation violate a copyright holder's rights, but so would subsequent domestic resale of any such book. So e.g., if I sold Half-Priced Books a book I bought in Europe (which I've done), and they resold it, both those sales would be illicit, absent publisher consent.
Obviously the real target of the publishers' suits is cheaper versions of books (mainly textbooks). But I don't see how the arguments they're making can be limited to that case, and wouldn't also sweep up a whole bunch of other reasonably common cases where people sell books in one country that they bought in another country. Some examples: estate sales of people who grew up in one country and died in another one; resale of books bought on trips; small-scale independent importation and sale of books that were never published in the U.S. (e.g. novels in the original French/German/etc.). Heck, as an American expat in Denmark, I fairly routinely sell U.S.-bought books in Denmark or vice versa, depending on where they happen to be at a given time and how full my suitcase is.
The more suspicious part of me suspects that, while parallel importation of cheap textbooks is their main target, they wouldn't really mind an outcome that banned those other resales, either, and looked more like a region-coding system. For example, one easy-ish thing Half-Priced Books could do to keep safe would be to filter by ISBN, only stocking books with ISBNs indicating US publication. That'd have some false positives (some foreign-published books are imported with the publisher's blessing), but it'd be more feasible than attempting to determine on a case-by-case basis whether a particular book had undergone an authorized domestic first sale.
An alternate statutory fix that targets only the narrower case could be to legislate: 1) resale of any lawfully owned book in the U.S. is legal, regardless of where it was first sold; but 2) large-scale [for suitable definition] parallel importation with commercial intent is separately prohibited.