From somebody outside the social media echo chamber (i.e. a user, not a maven), this seems like a tempest in a teapot. I'd welcome some elaboration.
It can't do that for twitter. It doesn't know your twitter ID, nor does it have access to your twitter network. It can crawl all the twitter pages just as it crawls the rest of the web but that may not be as relevant as the search results from your network (and hence rightly may be ranked lower).
If twitter wants to appear alongside your Google+ results, they would have to open up their twitter social graph to google (or any other search engine) so that google knows who you are and can produce results accordingly.
As a user I think this is good. I don't like the idea of my data being held hostage by sites.
https://plus.google.com/connectedaccounts
And because Twitter is largely public, Google knows who you follow and will show tweets and links in serps. Has done for some time now.
You can tell Google who you are on github, but I haven't noticed any interesting search results.
You right about password protected content though. You can tell Google who you are on Facebook but it can't crawl most of the data.
It is a tempest in a teapot.