fix invalid recaptcha token

Lets say there is a site called [login to view URL] The site [login to view URL] has a recaptcha that needs to be solved somewhere. What I want to do is not solve the recaptcha on the site but rather solve a recapcha hosted locally and then pass the token. In other words Im solving somewhere else. Obviously I'm using the same sitekey. Why does this not work for all sites? Whats confusing to me, is when I use a captcha solving service like 2captcha, they provide a valid token but when I solve locally, it doesn't work. (I can solve but token isn't valid). I'm thinking it has to do with the domain its being solves on. How does 2captcha do it then? I'm sure they don't open the page and solve and give me a token. I'm thinking maybe it's somewhere in the request while solving that you tell google which domain you're on. Please help me with that :)