PACE accounts are front facing @vt.edu addresses backed by an Exchange Resource Account or a Google Group. The group is able to send email using "Send As". If only one member of the group is able to "Send As", you have a permissions issue.

Check not only that the group has "Full Access" permissions, but also "Send As" permissions. If only one member is able to use the "Send As" feature, they are likely the owner of the group.