HTTPS doesn't work like that - it isn't a check or balance on the quality or provenance of things you receive via HTTPS.
An https connection is an http connection encrypted with a server certificate, and means that, for that given connection, only software and organisations your trust can read that data.
A valid server certificate (that is, an https connection that doesn't generate an error in your browser) means only one thing, in general terms: something you trust (your browser) trusts something else (your operating system) trusts something else (your operating system vendor) trusts something else (a root certificate provider) who in turn sends 'trust' down to the person you're connecting to.
That chain of trust usually means that people can't fake an https session - usually, the chain of trust and network path go via different organisations (except at the endpoints), and that means that https is secure in most typical scenarios (and is why organisations can snoop on your https traffic at the proxy server - your admins can inject their certificate at the 'your machine' level).
So, given all that - what is it actually good for? Well, an https connection means you're overwhelmingly likely to be talking to the entity you think you are. That doesn't make their servers or networks any more secure however - if someone is able to get into the bank's site and change contact details, well, https isn't going to help since they can change the http and https sites.
Coming all the way back, what does this mean for content on the internet?
Well, https is a technical implementation of a chain of trust - since you can't verify who I am, even if there was an https connection between me and http://security.stackexchange.com/, you still don't have any reason to trust me, or any of the information I'm proving you.
You can, however, verify your bank is who they say they are - they know things about you noone else knows (such as a code they sent you via regular mail or the account numbers on your statements) - so the fact that you used that code to log in, or that the account numbers match your bank statements means that you believe they are who they say they are. https then provides you a mechanism for leveraging that trust - you're comfortable they are who they say they are, you trust them via a technical chain of trust and that chain encrypts your communication so your network layer can't read into the conversation.