Clipping border (Alt B) makes a dark box around the selected area:
Setting the background color to the same color as the box doesn't work if you have Only render enabled.
How to make the box transparent instead?
There is a setting for 'Clipping Border' now in newer version of Blender. themes / preferences / 3dview / clipping border color option box. The default color is a dark grey, and the setting for transparency is called 'A' for Alpha Value. The default Alpha is 1 which is Opaque, if you move the slider to '0' the View Clipping Background is Transparent!