Actually there isn't a 4th button listed that I can see in 1.03u.
The problem isn't that the 4th button is missing, though, it's that it's mapped weird within MAME. On the arcade CP, the "Quick High Attack" button (button 1) serves double-duty as the start button. For some reason within MAME this button is mapped as the Start button and not as button 1. This leaves the 3 buttons remaining. Of course this can be re-mapped, but it's annoying. TMNT uses a similar setup, but MAME correctly maps the first button as button 1. Pressing start button does nothing in TMNT.
I'm guessing this isn't deliberate and is a mistake that should be corrected at some point. According to MAWS, PR was added in version .60 and hasn't had any changes since.
Primal Rage was a great game for it's time that had some original ideas and a lot of well-implemented borrowed ones. It doesn't hold up quite as well these days, but is still fun to play occasionally. Somewhere down the line I want to pick up the JAMMA PCB for this game since I use a PR cab as my generic JAMMA cabinet.