I would be cautious of normalcy bias.  We are dealing with iterated expansive maps.   Such systems can diverge rapidly.  It's a new technology and will introduce novel system dynamics.  Very few external analysts foresaw the collapse of the Soviet Union.  There is strong self-similarity in the price curve.  The manias seen so far may be higher order.  

If your log-logistic model is a MAP estimation, I would say it has strong empirical and analytic support, which would push the fractal fit (already quite unlikely, according to my own understanding, but still a possible expression of a distinctly conceivable set of dynamics) outside of the range of interesting possibilities.  But if log-logistic fit doesn't have a principled justification, with definable likelihoods (and I haven't seen that yet) then I would not exclude cascade models which typically produce such curves in other markets.  

You say that declining rates of adoption reversing would be unprecedented.  I say, how long have you been looking for them?  And, how many deviations lie between the current rate and the rate which would be implied by the fractal chart?   The history of AAPL comes to mind as a case of the former.  Regarding the latter, if it is within a couple of deviations, then it would not be surprising if the decline in growth were noise.  (And the more so, in a heteroskedastic model.)