There is a large discussion to be had and I do believe that I have some novel points to make on the subject, but what I would like to do at this point is note that just because you can't imagine another way that this could be done, it doesn't mean that it can't be done another way. You called this a fact, and that's a strong claim that I urge you to retract.
To approach this from a different perspective, imagine somebody saying the following at about 1890:
"This ignores the fact that if we ever do make a heavier-than-air flying machine it will either be via (a) reverse-engineering of birds or (b) some kind of evolutionary algorithm."
I think the misunderstanding comes from confusing "strong AI" with "human-like AI". It may be impossible for a meatbrain to build another meatbrain-like AI, but, if we are willing to compromise on that and make some AI that can function at or above meatbrain levels in some of their functions, we have already a couple examples of very clever parts we can, eventually, combine.
A recent post on LessWrong, http://lesswrong.com/lw/3gv/statistical_prediction_rules_out... , suggests that won't help much, at least for most people. Even when they have superior tools and information available, most people prefer their own, inferior, judgement.
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>If this is not amazing enough, consider the fact that even when experts are given the results of SPRs, they still can't outperform those SPRs (Leli & Filskov 1985; Goldberg 1968).
>So why aren't SPRs in use everywhere? Probably, we deny or ignore the success of SPRs because of deep-seated cognitive biases, such as overconfidence in our own judgments. But if these SPRs work as well as or better than human judgments, shouldn't we use them?
A standard alternative path to superhuman intelligence (which is the precondition for a singularity.. NOT AI specifically) is IA: Intelligence Augmentation. I.e., work on making humans smarter than they are. It's reasonable to say that the Internet has achieved a lot of progress in that direction already. Get brain/computer interfaces working, and suddenly everyone will gain 10 effective IQ points through instant access to encyclopaedias and calculators. Etc, etc.