I think the point is, you can always understand the basic physics of what the hydrogen is doing just by looking at the mass. As we want to define stars based on what the hydrogen is doing (when there is lots of hydrogen, including deuterium), Tim's point is that we can characterize stars just by the mass. Now, one may be skeptical that a pure theory model is really that reliable, but that would be a hard position to maintain, as stellar structure calculations have been staggeringly successful so far. So I think your question really comes down to the latter part-- how do we know if Jupiter has a core of heavy elements? Seismology is not the only game in town there, and I think Romanus' approach has greater promise.