Being granted asylum in one EU country (as is the case you are referring to in Germany) does not afford a refugee the right to travel to any other EU country. That, I'm afraid, is just more UKIP anti-EU BS.
There is an avenue by which a refugee can obtain German citizenship and then move around the EU at will, but it is by no means a simple process. From the BBC:
"A refugee granted asylum who has lived in Germany for six to eight years can apply for German citizenship if they fulfil a number of conditions. You need citizenship to be able to apply for a German passport, which would allow you the freedom to live, work and move anywhere in the European Union. Becoming a German citizen means a person has to give up their citizenship of another country, unless they have special permission to keep it."
The practical impediment to them moving to the UK, I suppose, is the Channel.
Nothing really to do with an EU Army, but important to maintain the facts in this post-fact world...