The jeyamohan's article and its wrangling is the folly of saying Sruti/Notes alone make music.
Tamizh works sangam, saiavite etc have as much metrical beauty, unique to the language as any other Indian language. So we have to bring in the time component as a fundamental component of music - the arrangement of syllables.
Current researchers ( Dr Nagaswamy) are saying tolkAppiyam has influences from nATya SaStra. In my opinion all treatises , since they are post facto - ( that is another biblical bias about our philosophies - that everything is known only the day it was revealed and written down!! - whilst the bible itself is not like that.) - they must have bean sourced from prevailing practices.
It is entirely possible, Bharata wrote his treatise from practices prevalent at that time, which could include a pre-existing tamizh practices as well and tolkAppiyam could pre-exist nAtya SAStra as well.
Here they discuss it:
https://youtu.be/u1S9GGdcz60?t=595 . The tamizh scholars want an earlier date for tolkAppiyam. Not sure if any evidence can be found.
Dating in Indian history is still a controversy!
But whether which grammar pre-dates which other is not that important. The fact is grammar can be written only after the fact. We seem to lose sight of it.