I cannot reproduce Bronkhorst's complex arguments for the relative dating of Sp and Pp, but he concludes that the recension of the Pp that has come down to us is older than the recension of the Sp. Bronkhorst, as is his way, tells us his conclusion at the beginning: "I know of one plausible explanation: the Padapāṭha of the Ṛgveda was written down from its beginning" (p.184); and then offers his evidence.
The first evidence I have already mentioned: that the way we speak English is like the Sp, and the way we write it is like the Pp. He is suggesting that the relationship between Sp and Pp is just like the relationship between spoken and written English. The second is that the Pp contains some signs such as the daṇḍa (punctuation mark) and avagraha (similar to an apostrophe for noting elisions: like n't for not) which only really make sense in writing - they have no phonetic value of their own, and do not affect pronunciation generally. Like English punctuation they make reading easier. Bronkhorst also mentions a rule in Pāṇini's grammar which relates to the use of iti in more or less the same way as Western scholars use sic. He says:
"Pāṇini puzzles over the question of how the [manuscript] of the Ṛgveda (= Padapāṭha) must be read such that a correct recitation (= Saṃhitāpāṭha) is the result." (p.185)This suggests that Pāṇini is likely to have been working with a written text.
As Bronkhorst himself says, there is no unanimity on the date for the beginning of writing in India. Bronkhorst himself opts for the case made by Bühler  who places the date at about 800 BCE.
"If we accept Bühler's ideas, and estimate that it took the Brahmans about a century to adopt the alphabet and adjust it to their needs, the earliest possible date for [the written text] becomes 700 [BCE]. A later date must however be prepared." (p.186)Perhaps Bronkhorst reflects the state of knowledge at the time he was writing, though it is hard to imagine 78 years having passed with no contribution. In any case the subject has definitely moved on since Bronkhorst's article. Compare Richard Salomon in Indian Epigraphy :
Bühler's suggestion of an early date of ca. 800 BC, or possibly earlier, for the 'introduction of prototypes of the Brāhma letters' in India is hardly plausible in light of modern knowledge, but more cautious estimates such as that of A. B Kieth  that 'the real development of writing belongs in all likelihood to the fifth century' are not unreasonable. (p.13)Salomon points out that both the literary and epigraphical evidence is "vague or inconclusive" (p.12). It is rather more conventional to date writing in Indian to the 4th century BCE because this is the earliest date that can be confirmed by inscriptions minus a century.  (This practice of adding or subtracting a century to allow things to develop is pretty standard for scholars, though I sometimes wonder how justified it is!). However Salomon (p. 12) notes that pottery shards with Brahmī script writing found in Sri Lanka in the 1990's are variously dated to the 6th-4th century BCE, with most recent articles opting for the later end of the spectrum (i.e. towards the 4th century). 
Writing did not develop spontaneously in India, but was adapted from outside models. There is ample evidence for contact between India and the rest of the world. Already by the time the Buddha was born (ca 480 BCE) the Achaemanids were exacting tribute from the north-west of India (as far as the Indus River), and possibly were a substantial presence. As proof of contact Bronkhorst cites the Biblical mention of aloe-wood in Numbers (xxiv.6) which may date from between 900-722 BCE. Unfortunately the materials used for writing in India were not always durable, and stone inscriptions were not widely used until the reign of Aśoka (who may well have been imitating the Persian kings in his inscriptions).
The earliest form of writing we know about is the Kharoṣṭhī script which is clearly modelled on the Aramaic script used by Achaemanid Persian administrators. The Brahmī script is less clearly modelled on an outside script, but most scholars still see a relationship to Aramaic. I accept the arguments of Steve Farmer and Michael Witzel that the Indus Valley script is a form of graphic communication, but does not represent language - i.e. it is not writing, but similar to graphic signs in Sumeria about the same time.
The received tradition is that (religious) Indians were not interested in writing because sacred texts were memorised and passed on orally. Though of course this does not explain why merchants and administrators would not use it, especially when they were in direct contact with cultures that did use writing much earlier. Although the evidence for an absolute date for writing in India, after more than a century of study is, in Salomon's words "disappointingly inconclusive"; and although Bronkhorst cannot establish a relative date for the Ṛgveda Padapāṭha, except in relation to the Saṃhitāpāṭha, we see in his article a contradiction of the old chestnut that ancient Indians were not interested in writing. The Ṛgveda was written down early on, probably by the time of Pāṇini, which suggests that writing may well have been in use during the life time of the Buddha, or not so very long afterwards. The writing down of the Buddhist canon in the 1st century BCE, therefore, was not the radical innovation that it is sometimes portrayed as. As the recent discovery tells us, writing may have been in use in Sri Lanka for 3 or 4 centuries by that time.
What Bronkhorst shows is that the relationship to writing may have been more complex, both at any give time and across time, than we generally think.
- Bronkhorst, Johannes. 1982. "Some observations on the Padapāṭha of the Ṛgveda." Indo-Iranian Journal. 24: 181-189.
- Bühler, Johan Georg. Indian Paleography, edited by John Faithful Fleet. Bombay: Bombay Education Society's Press, 1904. (Reprinted by Oriental Books Reprint Copr. 1980)
- Salomon, Richard. Indian Epigraphy: a guide to the study of inscriptions in Sanskrit, Prakrit, and the other Indo-Aryan languages. Oxford University Press, 1998. [This is an excellent and authoritative guide to the history of writing in India]
- Salomon is citing from E.J. Rapson (ed.) 1922. Cambridge History of India, vol. 1 'Ancient India'. Cambridge University Press, p.126.
- e.g. A. L. Basham. The Wonder that was India. 3rd revised edition. Rupa & Co. 1967. Writing is down played to the extent of not being mentioned in many histories of India, e.g. Stein, Burton. A History of India. Blackwell,1998; Thapar, Romila. The Penguin History of Early India : from Origins to AD 1300. Penguin, 2002.
- I've seen the 6th century figure seized upon and used as evidence of Brahmī being invented in Sri Lanka.
- A good place to start is Farmer, Steve. A One-Sentence Refutation of the Indus-Script Myth. 2005-2008; also excellent is Steve Farmer, Richard Sproat, and Michael Witzel, The collapse of the Indus-script thesis: The myth of a literate Harappan civilization. Electronic Journal of Vedic Studies 11-2 (13 Dec. 2004): 19-57.
image: Ṛgveda Saṃhitāpāṭha 1.1-2.