This component of government grants is not broken down on the source I provided, but it is explained in the notes to universities' financial statements. See for example those of Australia's largest university, at p 66 [2]. $345 million was provided under the Commonwealth Grants Scheme, compared to $214 million under HECS-HELP and $58 million from the Australian Research Council (research grants are also provided by other bodies such as the NHMRC). The CGS is the means of funding CSPs, not a source of research grants [3].
Your original point, that 'international students make up more than half of the funding-through-fees,' might actually be correct even if you accept that payments under the CGS are on account of 'fees' (which is the language used in [1]). It is correct at Monash, where international student fees generated $653 million, compared to $1.03 billion from the Australian government including CGS, HECS-HELP and research grants. Monash is an outlier because almost half of its students are international or offshore [4], but it leaves me unsure as to the reliability of my original source. We can certainly agree that international student fees are a very substantial source of income, but I wanted to correct the common misconception that HECS-HELP loans are the sole source of domestic tuition funds.
[1] http://studyassist.gov.au/sites/studyassist/helppayingmyfees...
[2] http://www.monash.edu/__data/assets/pdf_file/0011/844508/mon...
[3] https://www.education.gov.au/commonwealth-grant-scheme-cgs
As for HECS-HELP loans, this is quite different from a subsidy. It's a loan from the government that has a guaranteed return (pretty good deal for them). But even from your own source, international student fees are 18.8% and total "local" contributions (including HECS loans) are 19.9%. Which is effectively what my original point was -- approximately half of the funding directly from students is from international students even though much less than half of the students are international students (I never said that 50% of total university funding is from international students, please re-read my comment).
If you are a local student and you don't use HECS you still only pay <25% what an international student would pay -- because they have a different per-course-unit fee structure that's far more expensive.