If the photos are exact or "slavish" reproductions of flat (2D) art, then under Bridgeman Art Library v. Corel Corp., 36 F. Supp. 2d 191 (S.D.N.Y. 1999) the photos are not original, and have no copyrights of their own. If the art was not under copyright (for example published before 1924) then neither are the photos. If the art is still under copyright, the photos are "copies" and the permission of the copyright holder (of the original art) is required unless they fall under the fair use exception, which photos taken for and used in classroom instruction, and for no other purpose, might well fall under.
However, if the photos are so taken that angle, lighting, filters, and other aspects under the control of the photographer make a difference to the photo, then they will generally constitute new works, and if the art is under copyright protection, will be derivative works of the originals, and both the copyright holder on the original art, and the photographer will hold rights.
One rule of thumb is if the photo shows the frame of the painting, it probably has original elements of lighting and viewing angle. The more the photo approximates a scan of a flat work of art, the less original it is.
Photos of sculpture, architecture, and other non-flat (3D) art works (and objects) inherently involve artistic decisions about viewing angle, lighting, etc, and will pretty much automatically be original enough for copyright protection.
If the original art is out of copyright but the photo is an original work the photographer will hold rights, but no one else will (unless the photographer sells or transfers the rights). In that case it does not make much sense to call the photos "derivative works" as that term is intended to indicate that the works are subject to another's copyright, which these are not, because there is no copyright on the original. Or one could call them derivatives of a public domain work -- the effect is the same.
Under the case of Feist Publications, Inc., v. Rural Telephone Service Co., 499 U.S. 340 (1991), a work must have a certian minimum degree of originality to be protected by copyright under US law.
Both Bridgeman and Feist are US cases, but many other countries have followed their logic and apply similar rules to copyright issues.
It is not uncommon for those who have taken photos of art to assert copyright protection which a court would not uphold, but this will not be judged unless someone copies these photos, and the photographer (or someone claiming through the photographer) sues, and then defense challenges the validity of the asserted copyright. The statements in the text quoted by the OP may be based (in part) on such untested assertions of copyright.