In this case, I’d say the “rather than” means: if at all possible, use Fiverr’s system. Else, the ToS bits about privacy (no email but just a download link), not trying to circumvent anything, and providing files/proof of delivery apply.
Also, I’d “rather” stick to solutions that have been accepted in the past and not try anything new without getting the OK from support first.
edit: If someone uses Dropbox because they like it better, even though the file could be sent with Fiverr’s uploader, it might be interpreted as “circumventing”, depending on the person, I guess. As always, whatever you do, do it at your own risk and peril.