The cover art is embedded in the epub file by the publisher. If the publisher's ebook edition cover doesn't match their print cover it's probably because they don't have (and didn't want to pay for) the digital rights to the cover art.
If the cover art is correct on Kobo, where I bought it, and shows up properly on the Kobo desktop application does this still apply?
(I've moved my books to ADE because the Kobo desktop application is giving me nothing but trouble but I really like having the proper cover art)
Thanks for your answer.
No Kobo experience here, sorry.