Symptoms

User does not have access to Appit features that are a part of a solution on a given site collection.
 

Diagnoses

The user's account must be added to the correct group, namely one that has Solution Participant rights. Which groups are assigned these permissions can be found in Appit Admin > Configure K2 Permissions. Once added to the appropriate group, a group sync must be performed to update Appit so that it recognizes the change (found at Appit Admin > Synchronize Groups)
 

Resolution

Added user account to a group with Participant Rights on the site collection and ran group sync.