Correct me if I'm wrong here but I believe that then all one would need to do is stick an SSL intercepting proxy (such as http://mitmproxy.org/doc/ssl.html) in the middle and get the keys from there.
If the client just sends the secret as part of an authentication request, then a proxy would reveal it. But if some form of challenge/response [1] process is used, where the value sent is derived from the secret and an unpredictable challenge sent by the remote service, then as far as I know a proxy wouldn't help.
I don't know enough about the details of the Twitter/DropBox/etc APIs work to know if they use challenge-response.
[1] http://en.wikipedia.org/wiki/Challenge%E2%80%93response_auth...
For what happens in the real world, see Georgiev et al.'s "The most dangerous code in the world" at https://crypto.stanford.edu/~dabo/pubs/abstracts/ssl-client-... (spoiler: I described this paper in our internal knowledgebase as "very readable. Promises lots of facepalming and delivers in spades.")