And yes... this is the official agency for ISBN in the US; the International ISBN page only looks a little less scammy: https://www.isbn-international.org/. Maybe they care more about analog media than digital...
This is not exactly what the page says. It says nothing about them be free to give the same ISBN to someone else.
Typical case: a publisher gets hundreds of ISBNs in bulk. At some point they close their business. The agency can give the unused numbers to someone else. Determining which were unused is not always easy, since there is no requirement to inform them when one is assigned to a book -- therefore mistakes are made. The end result is that re-use is possible (and actually happens).
In the end it's just some number on a book, but in an ideal world a ISBN is not reused and only assigned to one book.
What can be done when a book is printed with the wrong ISBN?
A new, unused ISBN must be assigned to the book, stickers or labels made and placed on the books, and all industry databases updated with the new, correct ISBN
[0] http://www.isbn.org/faqs_general_questions
And yes... this is the official agency for ISBN in the US; the International ISBN page only looks a little less scammy: https://www.isbn-international.org/. Maybe they care more about analog media than digital...