Is it possible to make oauth secure on iOS?

I am investigating OAuth 2.0 as a means to implement single sign-on + authorization for a "suite" of iOS apps. To explain my concerns, I'll simplify and use Facebook + a 3rd party app that uses Facebook for authentication (let's say Words/"Words with Friends").

For the purpose of example, I'll assume that Facebook registers to support scheme/protocol "facebook://" and that Words registers to support "words://"

I also make the assumption that it is not possible to secure the "client-secret" or the protocol in an iOS application because you can decompile the application. Any ways that I have come up with to secure this results in security by obscurity.

Another assumption is that there is no way to prevent two applications from registering to handle the same protocol. The behavior when two apps both register for the same protocol is indeterminate. (Although it appears that the first app to launch on the device gets registered while the second apps registration is ignored)

If I understand the workflow between Facebook (user-agent) and Words (client) on the iOS device:

User launches Words
user chooses to logon via Facebook credentials
Words invokes openUrl("facebook://") which contains, among other things an identifier for Words as an application and a redirect uri (i.e. "words://")
iOS launches Facebook application
User enteres credentials, which Facebook application validates against Facebook authorization server.
User prompted to authorize Words to access Facebook data (i.e. Words can access my friends list)
Facebook invokes callback uri provided by Words along with access token (i.e. words://access_token?token_here)
Words uses this token to access my friends list (i.e. protected resource data)

Assuming the above is correct, if I want to be malicious and access random people's friends list, I could create an application that also registers to handle the protocol "words://" and get it on the app store. If someone has my app and Words installed and my app is the one that successfully registered (i.e. launched on the device before Words), then:

Launch Words, choose to logon, launches Facebook
user authenticates / authorizes
Facebook attempts to redirect back to Words by invoking openUrl on the redirect url
My App (not Words) is launched
My App now has access to the auth code, which (with the secret learned by decompiling) can be exchanged for an access_token, with rights to access your friends list

I am hoping that my reasoning is flawed above or I would have to conclude (specifically) that Facebook iOS authentication for 3rd party apps is insecure.

More generically, is it possible to implement OAuth 2.0 (authorization/implicit grant workflows) securely on iOS application?

Google has come up with an experimental solution for this problem that they call OAuth 2.0 for Installed Applications.

The Google OAuth 2.0 endpoint supports applications that are installed on a device...it is assumed that these applications cannot keep secrets.

Essentially, the shared secret is treated as non-secret.

At the time of this writing, most OAuth 2.0 servers do not seem to support this experimental design.

This design introduces the risk that an attacker could create a new client that represents itself as your application to the authorization server (the attacker would need to obtain the client identifier as you describe in your question, or by following one of the techniques suggested here).

However, this risk seems to be mitigated by the fact that the resource owner (the user) would be unlikely to authorize the malicious application to take any action on protected resources, since he/she will know that the application is not, in fact, your application.