I've found a solution for this but it is very component specific.
I'm working in J1.5 and needed to add some ACL functionality.
Therefore I work with DJF ACL.

My problem was that the user called the mediamanager was prevented to execute task connector.
If you look in the code of:
administrator\components\com_k2\views\media\tmpl\default.php.
Line 16 is calling a task called connector.

Since I prevented execution of this task, the message:
Invalid Backend Response - Data is not JSON.

So if you are using DJF ACL, try this. If not, maybe it could be a ACL problem if you are working in J.16 or higher.