Interesting, I had gotten the impression Twitter was aligning itself more with DataSift in recent years. I used Gnip a few years ago and thought it was a great service, although the high price point drove us to ultimately roll our own.
Yes, Twitter streaming API plus several other data sources (Facebook, Reddit, forums, etc.). It's enough for us since we're always filtering by keywords or users. We were also granted elevated access.
It was pretty straightforward in our case. We had to show them that we had use cases that weren't feasible with the default access level and also demonstrate that we weren't competing with their user experience at all. Not sure how much it mattered but we had been using their streaming API for almost as long as it existed.
I had the same question when I read this. The streaming API is only a fraction of the data offered by the firehose, but that's not as much of a problem in every use case.