Update: unfortunately some parts of my original post right below are not correct, confusing or misleading - you will find a much more accurate description of my problem in my second answer to Trudy's response further below!
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Hello everybody!
I'm getting crazy about this one so maybe someone can help me with this:
Kanban boards do have this great feature called "Kanban backlog".

Thanks to this feature the backlog items will not get displayed on the first column of the board. Instead you can use the "backlog area" to organise the backlog "behind the curtains"- perfect!
What I absolutely do not understand is why Scrum boards behave differently in this regard - it makes me go nuts, that I have to map a status to (usually the first) column of the board. As a result, all items listed in the "backlog area" of the Scrum board are getting displayed on the board itself as well - holy moly!!!

The backlog items should not be displayed on the board. They should stay in the background, in the "backlog area". There, only items dragged into an active sprint should be displayed on the board.
There even is a support entry that suggests, JIRA would work this way (here).

But it doesn't (and contradicts in a certain way the other support entry listed above - or at least it leaves out, that the "Backlog list or planned sprints list" will be displayed on the board as well).
Is there any way to make a Scrum board behave this way? The current behavior seems like a huge design flaw to me...