Make it possible for Org admins to see the user's details regardless the domain related to their account

Problem Definition

With the recent (May 2019) changes to privacy settings of Atlassian Accounts the users' details can be set to:
Anyone - This information is visible to anyone who can view your content, which may include people outside of your organization. For example, if your admin has set up Jira to allow anonymous access, then anyone who browses to your Jira issues can view this personal information. This information is also accessible by apps installed in Atlassian cloud products.

The name of your organization - This information is only visible to other users managed by your organization. Typically, this is anyone who shares your organization’s email domain, such as acme.com.

Only you - This information is only visible to you. (This option is offered on a few fields.)

Source: Update your profile and visibility settings.

The information displayed on the user's profile at https://id.atlassian.com make us believe that the privacy setting is applied based on the Organization the user is part of not the domain specifically as we can see in the screenshot below:

However Org admins that are not tied to the verified domains of the Org can't see the users' details when set to The name of your organization.

Suggested Solutions

Make it possible for Org admins to see the user's details regardless the domain related to their account.