Closing Apps with iOS7

I'm a little confused on completely closing apps on the iPad. Apple Support told me that all you have to do is to tap the Home Button 3 times to close all Apps running in the background. But what I see on the web is that if you tap the Home Button two times, you can see all the Apps that are running in the background and you can close them by swiping them up and off the screen.

So,,,,, I push the HB three times and then two times and it still shows that some Apps are running in the background.

Also, if I reboot the iPad and then hit the HB two times, it shows Apps still running in the background.

What is the real story? How can you REALLY completely close an App so it isn't running in the background?

I'm pretty sure that triple clicking the home screen actually gives you options for accessing accessibility settings. So, I'm not what the support tech is talking about. Plus, if that were the case, that would be an awkward design choice - a one click difference between close one app and all apps would be dangerous.

To answer your question, the double tap and then swipe up is the way to go.

I don't find triple click very useful myself. User can assign different actions to triple click, but I just Googled again and still can't find a comprehensive explanation of triple click that matches my iOS 7 iPad. I avoid clicking the home button anyway, for fear of wearing it out.