Why do British people think Americans support the PIRA or the RIRA?

I'm in college right now for engineering. I take classes with a lot of foreigners. I was talking with a couple of guys from London who accused Americans of supporting IRA activity. If there are any British on here, please explain to me where this notion comes from. The reason I am so shocked by this accusation is because I am very familiar with American ignorance. Most Americans cannot find Ireland on a map. Most don't even realize there is a difference between Northern Ireland and the Republic of Ireland. I also have to wonder how you can feel this way when the main IRA gun runner, George Harrison, was arrested by the FBI and given a 7 year prison sentence.