I had this issue with GoToMeeting. Requesting access to the Microphone was easy, and the app showed up in the list so I could add it to the preferences, but trying to add the camera navigated to preferences without adding the app to the list.
Tried rebooting, uninstalling, deleting preferences, etc. Eventually I left the meeting and opened the app preferences (app name > preferences in the toolbar), and when I went to change the video settings the request popped up again to update privacy settings, only this time it added the app to the list in preferences (previously it would go to the list, but no app, no box to check).
Seems like there is something keeping the app from requesting access to the camera and adding its name to the list, given the range of apps that experience the issue. Eventually I was able to add it to the list, but it took over an hour of troubleshooting before the app finally showed up, and I don't believe any of the common troubleshooting (reboot, uninstall) had any impact.