I've just checked, and the (Linux Firefox) camera/mic permissions menu fails to appear on the other WebRTC conferencing sites linked in this thread, too. So it's definitely not just appear.in.
[Edited to add:] For others suffering from the same problem, the bug report linked in parent suggests it may be fixed in FF 27, which will apparently be released during the week of Feb 4th.
Firefox 26 on Debian Linux, however, never shows the prompt. The appear.in page just asks me to use the menu that should have (but didn't) appear.