In the assignments tool, if I go in as a maintainer and remove the submit permission for those with access privs and then log in as a student, go to the assignments tool, I see the list of assignments, but the titles of the assignments are invisible. Since the read permission is enabled in this case, those with access privs should still be able to get into the assignments tool, view the titles of their assignments and even read the assignment itself, just not submit. See screenshots for illustration.
asn-SubmitEnabled.jpg - What a person with access privs sees when both asn.submit and asn.read are enabled
asn-SubmitDisabled.jpg - What a person with access privs see when only asn.read is enabled