The availability of the copyrighted works is not determinative. Fair use in the US takes (at minimum) four factors into account, listed in the federal copyright statute: https://www.law.cornell.edu/uscode/text/17/107.
That quote from Stanford's library is not discussing fair use doctrine in general, but rather is stating what is permitted in those specific circumstances. There are plenty of instances of fair use where the underlying work used was available at a fair price. That's the whole point of fair use law: some use of a work that is facially infringement escapes liability because the particular use is considered fair.
Current US copyright law is not clearly in a place to view model training as infringement. Courts have a long history of permissiveness in the face of copyright challenges to new tech (e.g. the image search engine cases, Google v. Oracle and smartphones, Sony v. Universal and VCRs) and I predict it will happen again with AI. The cat is out of the bag and judges know that finding training to be infringement of each training example will have a negative impact on a new product category. If training was more obviously infringement then that permissiveness would be harder to sell, but in my opinion it's really difficult to argue that a "copy" of an example has been made during training (aside from the copy made to process the example).
Another aspect of this arrangement: you don't pay federal income tax on money you receive as a loan in the US. The money does not count as income because of the matching obligation to pay it back.
That quote from Stanford's library is not discussing fair use doctrine in general, but rather is stating what is permitted in those specific circumstances. There are plenty of instances of fair use where the underlying work used was available at a fair price. That's the whole point of fair use law: some use of a work that is facially infringement escapes liability because the particular use is considered fair.