You can't download the
private part of the TLS certificate by pretending to be a browser. You can't publicly download it
at all. Your browser comes with a chain of
public certificates from reputable CA vendors, and you verify that a site is who it claims to be by using their
public certificate (which your browser downloads).
The only way they can succeed in proving who they are, is if their server has access to the corresponding private key of the certificate, which is why you can't spoof a properly secured site unless you either hack their server, crack the encryption, or install your phony certificate on the client (which is what corporations sometimes mandate). That's it.
It's been 17 years since 2000. Whatever security hole you may have used (if any) has long since been patched. The weak cyphers used in some SSL versions which you may have depended on are mostly gone (certainly from high profile targets).
If what you state is true, now in 2017, then there would have to be a huge conspiracy which involves all browser vendors (including Mozilla), as well as all national governments and the EU that hides this fact from the people. All software developers who do catch on (the relevant source code is open source after all) would have to bribed or threatened into silence too.
You are either misinformed or consciously spreading misinformation.