I've never heard of this either. Tor and VPNs are meant to protect you against this sort of stuff and I doubt even the CIA can find this info if you're smart enough (though I believe VPNs can accidentally leak your IP in some ways). What you might be thinking of is browser fingerprinting though which can be very useful to catch alts and just using a proxy won't help you (and I think this should be on the new forum). You might use a different IP for your accounts but you almost certainly won't be using a unique PC or browser for each of your alts and accounts could be collated and searched by them and cross referenced with other data etc.  

The WebRTC vulnerability could give away your real IP address.  Even if there were no vulnerability, it could come down to how the VPN is set up.  Are they using tunneling?  If not, then everywhere you surf could see your real IP along with the IP of the VPN.  Is the VPN including your IP in their header?
Even if the VPN were locked down and no trace of your IP were leaking, this doesn't mean you can commit nefarious acts online without getting found out.  There are log files on every server.  The amount of time logs are kept varies.  With enough resources and legal action, log files from VPNs could be turned over to authorities.  Once they see your real IP, they simply subpoena your ISP and will find out who you are.  Realize that it can be more complicated than the scenario I use above, but my example is to simply help you understand that you're not truly hidden online.