It isn't necessary to do B Med Sci to get into a graduate med program. Graduate medicine admission is open to students with any bachelor degree and offered on basis of GPA, GAMSAT and interview performance.
The combined medicine program at USYD offers combinations to a huge variety of degrees like B Arts/B Economics/B Business/B Music in addition to B Sci (adv) and B Med Sci. It shows you that students in the graduate medicine program, at USYD at least, come from enormously diverse backgrounds. The degree resolution for the non-science combinations may give you an idea of what the medicine faculty expects from students entering the graduate medicine program - basically, all the students in the non-science combinations have to complete 6 credit pts (so one subject) each of 1st year biology, chemistry and physics. And the last section in the GAMSAT tests general science knowledge related to these areas. So whatever degree you decide to do, you should consider choosing these (maybe as electives).
You said that you haven't done any science subjects in the HSC - what was the reason for that? If you're not interested in science, then a science degree (or even medicine) may not be right for you. If at the moment you're only concerned about getting into graduate medicine, then think carefully about what your interests are and pick a degree that will allow you to study the subjects which you like and will excel in, for the sake of a high GPA at least. So do arts, or music, or whatever you will really enjoy. It also makes sure that if you happen to change your mind about medicine later on, you won't have wasted all the effort of preparing yourself and then realising that it's not what you really want to do at all.