SharePoint 2013 search results will not be displayed for partial users

Question

one of my customer runs a Sharepoint2013 Server. this Server runs with an Membership provider and provide a custom user database (ASP.Net Membership Provider).

It will hold many users (about 25.000 users). These users will be distributed into several Groups with the same access rights like the default SharePoint Visitor group. These Groups will have access to the News List (A libar with pages).

Each group is below the limit of 5.000 Users.

Let's assume we test it with two users (User A and User X).

We created a search result webpart, that will display the articles from the "News" list. User A will get the result displayed correctly. All of it is perfect.

User X not. Both users have access to the news site pages, but they won't appear on the search results.

What I have done:

• Checking the Access rights They have all the same rights, the user can all access the elements that must be shown in the SharePoint
• Checking the Results Yeah, the results will be displayed
• Did a FullCrawl to with an Indexreset before Yep 2 times
• Set the Search Config on the site It will search through all sharepoint webparts and it don't take any effect

For some reason, when I put any non working user into the default Visitor Group of the SharePoint, then it works like a charm.

But Why?!?

The Access rights are ALL the same. Is there a special site that must be accessible instead of the searched items?

I tested also with the pseudo user "everyone" then this problem was soled too, but this will take effect on an implemented system so that the user will get more Application-Acces as it is allowed, so that is not really an option. And also the working users are also restricted, but they get the results be displayed.

Does anyone can give me a hint, how to check the security in SharePoint (The crawler has complete access to the elements), or how I can analyse this special case? The ULS was not very helpful in this, because it will send only the message that now result was found.