Hi there Clyde. You're actually misreading the first quote ("If changing the cover of a book… no, a new ISBN should not be assigned.")
Admittedly, the ISBN.org site isn't very specific in their wording, but in that context "changing the cover" refers to changing the cover *content*, not the cover *type*.
5.4 Publications in different product forms
Different product forms of a publication (e.g., hardback, paperback, Braille, audiobook, online electronic publication) require separate ISBNs. Where electronic publications are made available in different file formats each separately available format shall be assigned a unique ISBN. (See section 6.3 for further information on dealing with e-book file formats).
That is why our site correctly states that you cannot reuse an ISBN between different cover types.