An undesirable side-effect of admins having view rights on all organizational content is that any item in the organization (including items not shared with the admin or items not even shared at all) is a candidate to appear in the search results for admins.
For example, there are several items with the keyword “Afghanistan” that have been registered by USER A in an org. These items have been shared by USER A only to a private group of which ADMIN B is not a member. However, when ADMIN B searches “Afghanistan” these items show up in their search results. Additionally, the admins actually see search results that include organizational items that are not shared with anyone.
I can definitely see the use case for an admin needing to quickly find a particular item in their organization, no matter if it’s shared with them or not; this is a nice feature from an admin point of view. However, admins are users, too – by that I mean that many people who happen to be in the admin role in their org likely also spend a lot of time just using ArcGIS Online to make and share maps and collaborate with colleagues. In this case these extra search results get in the way of their day-to-day work since they are items that normally wouldn’t be visible to them/shared with them.
I might suggest an “admin search” feature for consideration in a future release. This might be implemented like the “organizational search” has been with a checkbox on the search results page. The default would be for admin search to be off so that only results shared with the admin user are returned in search results.