That's not quite correct as stated. People usually try the local language first, if they can speak it at all. At that point they don't even know what each other's languages are. So two British people meeting for the first time in Germany may well start off by speaking German to each other. I've seen that happen a few times.

But I've also seen a German speak bad English to someone just because they looked foreign. They were foreign, but having lived in German for a while they could speak German better than they could English, and after a while they politely pointed this out. It was a bit embarrassing. It is definitely better to try the local language first.