You ignored the important qualifier at the end of the sentence: ...to enable Evernote to operate the Service.
And the preceding clause:
In order to enable Evernote to operate the Service, we must obtain from you certain license and other rights to the Content you submit so that our processing, maintenance, storage, technical reproduction, back-up and distribution and related handling of your Content doesn’t infringe applicable copyright and other laws.
You can't read half of a line of a TOS and assume it means something separate from the totality.
exactly right. Under US copyright law, Evernote could be deemed to violate your exclusive right (as copyright holder of your content) to make copies whenever they made a backup. So to avoid any opportunist litigation, you grant them a limited licence to copy your work. The same goes for your right to display/perform.
And the preceding clause: In order to enable Evernote to operate the Service, we must obtain from you certain license and other rights to the Content you submit so that our processing, maintenance, storage, technical reproduction, back-up and distribution and related handling of your Content doesn’t infringe applicable copyright and other laws.
You can't read half of a line of a TOS and assume it means something separate from the totality.