Yes, this works, but the trick is that you'd need a certificate and private key signed by a certificate authority that authenticates the specific location you are browsing to. This certificate has to be part of a certificate chain that leads to a CA certificate that has to be trusted by your browser. The video makes you believe that a CA has to say "yes" which is incorrect.
So lets go to real life scenarios. Basically there are two possiblities:
You somehow have a trusted certificate in your browser that authenticates your connection. This could for instance happen if you're browsing through a company proxy that also proxies the HTTPS connections. These proxies exist; they basically look at the content of the connection and then send it through the HTTPS connection to the server. The proxy then acts as a HTTPS client. In general the IT dept makes sure you've got a company or proxy specific certificate in your browser store. The connection would fail if you'd use a stock browser.
A trusted CA is compromised and gives out bad certificates, either deliberately or unintentionally. A good example would be the DigiNotar debacle here in the Netherlands, where DigiNotar signed an end certificate for google.com, among others.
In both cases an unaware user would be tricked into accepting the connection, even though the underlying certificate chain would differ from the original one. Closer inspection could however show that different certificates are being used then the original one.