The Stream will work fine with a 4-tuner Premiere. It would only take a tuner for "Live TV". The current implementation requires that a recording be started on the host box for the "Live" program you want to watch. To the user at the 4-tuner Premiere, there's no real impact, all they would see would be a recording active on the channel being streamed to iDevice. They can continue to use the other 3 tuners as they wish. The user at the Premiere could even watch that program at the same time if they wanted to. The Stream would then trans-code the recording and send it to the iDevice at a slight delay to real-time.
It does not "take" a tuner for already completed recordings. The proper comparison would be MRV or MRS between 2 Tivo boxes. All tuners are still available, the Stream is simply having the recorded program sent to it over the home network, and then trans-coding and passing it to the iDevice.