Reason I ask is on Twitter I set up notifications for guys I follow and when I get one through I click it but when I click it never takes me to the actual tweet but if I leave Twitter on in the background it works fine
Some people don't like Apple's answer for whatever reason so continue to ask the question.
That doesn't change Apple's answer.
We should move on from this discussion. It's a dead issue for Apple and whatever anyone feels about it, everyone is entitled to ignore Apple's answer and do what they feel is right for their own circumstance if they don't like it.
If you never occasionally quit all your background apps, you end up with every single one you've opened in the app switcher. This can be a major pain when it comes time to actually force quit an app, or shuffle through the app switcher to select an app. Countless apps zinging by in the app switcher, cluttering up the works.
Although quiting apps may not save you any power, doing so will clean up the app switcher. So that's worth it to me.... Even if it uses another mA of battery power.