The "magic" that allows all the things in the OP's statement to be true is that the FHA's Streamline program does allow the lender to roll a "interest rate premium" into the loan. That premium pays for all the 'savings'. It is spelled out on the FHA/ HUD site --
http://www.hud.gov/offices/hsg/sfh/buying/streamli.cfm
Frankly it might not be a bad idea if you can get your APR dropped by a full point (or even less), and with a 6% fixed loan when there are lots of loans available on the happy side of 5.0% that is fully understandable...
Off course if you have the funds available (and the house will appraise out and meet equity standards) to do a regular refi you MIGHT be able to get something as low as 4.75%, and depending on how big a mortgage and how long you'd have to recoup the refi costs in a normal loan that might make more sense.
Be very careful. I have seen more than a few folks get duped into working wth a "drag my feet" lender who pretty clearly is waiting for the rates to hit some "magic" spot to maximiize their own profit, and that is a very irresponsible game to play -- ultimately it an result in the borrower getting nearly no rate reduction and the lender getting a huge premium.