From a controller friend of mine.
The expectation is if cleared for the STAR (not to descend via, just lateral) and then told to “descend and maintain” an altitude where in the descent you’d intercept 280k then that’s what they expect you to do unless other instructions have been received. No matter where you are on the route, even outside of KOZAR. At a minimum the speed note applies to the entire STAR.
Makes since since the speeds and altitudes are separate parts of the procedure, speed is ultimately more important for separation.
Personally, I just verify if they want us to slow as published or just to make the first fix restriction.
If anyone finds a legal interpretation that contradicts this, let me know.