Sorry but I think you're wrong. When the team being supported is Great Britain then I'm proud to be regarded as a British supporter(Olympics, etc). When the home nations are competing then then it is no longer regarded as British but Welsh, Scottish, English, Irish.
Using your argument, would you be content for a news article to state that the Europeans are all rioting in the street even if it was only the French. Factually it might be correct but not an honest indication of the perpetrators.
Your second point is also flawed if you've seen the numerous clips and news articles coming out of Bordeux.
Don't get me wrong that I think the English fans are being treated unfairly as the Ultras are definitely instigating the violence...but still it's not the British that are involved.