Story details pane - "Attach screenshot" screen is broken

We use the "Attach Screenshot" functionality of JIRA (6.3.8),
and it works perfectly if we open up an issue and use the menu item More/Attach screenshot.

However if we try to use the same functionality on an Agile Board
("..." icon on the issue details panel and click "Attach Screenshot") it just does not work...
it does not open the usual dialog but a full screen where the Ctrl+V does not do anything and the screen looks weirdly broken
(see attachments)