The share links look like this

https:// send.firefox.com/download/<$file_identifier>/#<$encryption_key>

Data after the # in the url should not be sent to the http server by the client. Encryption/decryption is presumably handled in the users browser by JavaScript.

The statement about not having the ability to access the contents of the files is perhaps somewhat misleading as they do control the JavaScript that either creates the key or will be given access to the key when someone retrieves the file (by reading it off the end of the url).