Okay - glad to know it's a bug and happy to help find it.
I wasn't entirely certain I understood what your explanation meant. So I reevaluated the problem and found a partial solution (enough to solve my current issue).
For those who might find it helpful:
PROBLEM
I have two levels of "moderators" that I wish to be able to edit user profiles. The reason is that new user registrations must be approved, and there's an "interview process" that they go through. The first level moderators need to be able to edit the profiles of these "pending users" to fill out the "interview form". They should only have access to their part of the interview form and no other parts of the profile. The same goes for the second level moderators (access their form but not edit any other part of profile). When moderators view the profile of pending users they'll see a special tab which displays the saved information from the "interview" that has been entered.
PARTIAL SOLUTION
CB Conditional has the ability to display/hide tabs based upon usergroups. I made a new usergroup called "Applicant" which holds all new user registrations. Under this group are the two moderator groups, which we will call "Level 1" and "Level 2" for this post. Level 1 and Level 2 are children of Applicant (but not each other). The Registered group is where the members reside, which is a child of Public. See the following for clarification:
Public
...|- Applicant
.......|- Level 1
.......|- Level 2
...|- Registered
...|- Guest
...|- Super Users
[periods used to ensure alignment, consider them spaces]
The special application tab (viewable on front end) contains only Custom HTML fields that read and display data from editable fields stored on restricted tabs. These other tabs are only viewable in the profile edit screen, and only by certain usergroups. The usergroups that can see these tabs are moderators (albeit separate levels). This allows Level 1 moderators to only access their tab while Level 2 can only see theirs.
Level 1, Level 2 and Super Users groups are included in an Access Level called Moderators. This AL is assigned in CB as the Moderators View Access Level in configuration. Level 1 and Level 2 have access to edit user profiles for those in Applicant, however they cannot edit each other as they're on the same level. They also cannot edit Registered as it is outside of their scope (this is desired).
The "partial" in the solution comes in here. They have full edit access to members in Applicant. In profile edit they have full access to all default tabs (Canvas, About, Portrait) plus their special tab. It was desired to have those default tabs hidden on profile edit so that they cannot change this information.
It was definitely possible to hide these tabs using CB Conditional. I could easily set it to "hide on profile edit if usergroups contains Applicant". However, as moderators are children of Applicant (so that they have edit privileges) it also hides their tabs rendering it impossible to edit their profiles (not desired).
HOPEFUL
I'm hopeful there's some way I can rig this to make it work 100% as desired. These plugins are incredibly powerful, it's just a matter of figuring out exactly what combination works. Any further insight would be helpful, but if not you may feel free to mark this as solved.