Love the wry humor . . .
. . . my reaction is that I'm always leery of any theory which is purely mathematical and takes no other evidence into consideration.
Yes, that is essentially my objection. It has other problems, though. It does not, to revert to my original objection, account for the aboriginal Australians. They arrived in the subcontinent 40,000 years ago. Their only close linguistic, genetic and cultural (as revealed by archaeology and ethnology) relations are the New Guineans and Papuans. The dingo arrived in Australia at some point between about 20,000 and 12,000 years ago. That arrival did not require intermarriage with whatever Austronesian people introduced it, but even if it had involved intermarriage, that's still well before the 7,000 year threshhold here. But more compelling is the fact that aboriginal Australians did not have any of the suite of domesticated plants, and no other domesticated animals than the dog/dingo which could have come from Austronesian people. They have no linguistic relationship to Austronesians (and even the highland New Guineans who live in areas into which the Austronesians never penetrated have loan words from one of any of the several Austronesian language family for Asian yams, or chickens, or the pottery or tool technology which diffused from the coasts). They had none of the technological artifacts of the Austronesians. They share no discernable genetic heritage with Austronesian peoples which postdate the migration to Australia of about 40,000 years ago.
The Amerindians present another problem for this thesis, as well. I could probably work up some more objections to the thesis, but given its basis, which as you point out is only mathematical, i will remain skeptical. I rather suspect that there is a great deal which they have not taken into account.
By the way, i learned for the first time recently that pottery first appears in the archaeological record 14,000 years ago, and in Japan. That is surprising, and significant. It predates the earliest evidence of the domestication of plants and animals, which was in the middle east a little over 10,000 years ago. More importantly, it means that the hunter-gatherers of Japan were sufficiently successful, and their environment sufficient provident, that they had a surplus which allowed the "leisure" to develop pottery, and to form settled villages. It should be obvious that itinerant hunter-gatherers aren't going to have any incentive to make pottery when it would just be something awkward to carry and heavy.