Not sure if it's the same issue you are seeing, but when I upgraded to 7.6, I found that process type actions have changed the way they interact with permissions. Specifically, I found that the check boxes for actions, including the default actions like edit incident, as now additive. That is to say that if the edit incident action has 'is edit action' and 'is admin action' both checked, then the user must have edit and admin permissions on the incident before that 'edit incident' link will appear. In 7.5 in the same scenario, a user would have only needed one or the other of those permissions, not both.
In case you are wondering, no, I could not find any documentation of this change in the release notes.