Its a bit tricky to get a user's credentials.
Here's what I think you can try.
Create a standalone app which can call any jive REST api (to start with, the ones you have mentioned).
Ensure this service has super admin access. So now obviously it can access all data.
Now when a user logs in, use the Jive api run as feature mentioned here --> Core V3 API - Run-As Feature & Signed Add-Ons
Make a call to REST api using the super admin account, but running as the logged in user's username .
If you see the documentation, you just need a username or userid, no password.
Use this to run as that user, and you can be assured only the content accessible to that user will be shown, though actually you are using a super admin account.
Hope you are doing good. Why are you not using oAuth and SSO, instead of passing user credentials.
I think matching usernames is a terrible idea probably not the best way to go about this. As Amit suggested using OAuth is probably the best approach.
I implemented this recently for an Office365/SharePoint application that used Jive data. You just popup the Oauth dialog once, and associate the tokens with the account of your current user in your application.
Actually, I submitted this as a topic for a session at JiveWorld, so maybe Ryan Rutan can approve my talk now, since there is customer demand ;-)