Is there any particular definition of "British English", or alternatively of "practically indistinguishable" and "nearly perfect equivalence", that one needs to be aware of to make sense of this paragraph? Because it's not making a whole lot of sense to me using the normal definitions of those concepts.
As for "Continental European, African and Indian English" - apart from the question of what those actually sound like, you intentionally refer to populations of which the vast majority speaks English only as a second language? Is it really fair to include those when comparing dialect sizes?
Edit: Also, while I will obviously defer to you as well as to RT on the finer points of Southern accents, his basic point - that at least some varieties of American English are closer to the English spoken in Britain several centuries ago than contemporary British is - seems fairly widely acknowledged? Wikipedia also indicates that "(...)spoken American English did not simply evolve from period British English, but rather retained many archaic features contemporary British English has since lost". Yes, he is wrong in calling it "Victorian" as it's older than that, but besides that it makes perfect sense to me.