then some device makes the requests out on behalf of the clients.

Well, that, or horribly mangles them. My employer uses Blue Coat ProxySG, and browsing Wikipedia in Chrome has been impossible for a few months. [1] Before that, it was anything which prioritized ECDHE ciphers and used Fallback SCSV, like the Mozilla Developer Network site. It's a pain in the butt.

[1]: https://code.google.com/p/chromium/issues/detail?id=511976#c...