A status page give you confidence that the problem indeed lies with Amazon and not your own software. I don't think it's very reasonable to notice issues, ask other teams if they are also having issues, and if so, just shrug it off and get a cup of coffee without more investigation. Just because it looks like the problem is with AWS, you can't be sure until you further investigate it, specially if the status page says it's all working fine.

I think it goes without saying that having an outage is bad, but having an outage which is not confirmed by the service provider is even worse. People complain about that a lot because it's the least they could do.