We use the URLReferrer and a code passed in on the query string to produce online videos so that only our paid clients can link to our video playback page. This system has
Your online research is correct. The main reason for not setting an HTTP Referrer header or equivalent is that this could be a security issue. The referrer contains "where you come from", this is private information, and should not be exposed to others, what use is it otherwise to have a secure site if everyone can track where you have been?
So: you cannot get the referrer if the referrer is encrypted (with SSL or otherwise).
Update: here's what the HTTP specification says about coming from a secure site:
Clients SHOULD NOT include a Referer header field in a (non-secure) HTTP request if the referring page was transferred with a secure protocol.
As you might have guessed, there's no way around this restriction. Your only option is to use a different verification model. One such method is giving your users a key and require them to send that as a parameter with the request. Several other methods can be thought of.