It stems from the idea that the EU marketed itself well by visibly sticking the EU flag on everything that is EU funded, and the reason why Scots, Londoners, Scousers, etc like the EU more than the UK gvt is that the UK government doesn't market the things it does patriotically enough.

Not saying its right, but that's the logic - its not meant to be some threat about withholding medicine, its meant to say "hey look, the British government does stuff too"