I don't understand your distinction between TA having validity...

I don't understand your distinction between TA having validity for a 'globally significant stock' and others - though I would argue that for extreme penny stocks TA is generally not used due to their inherent volatility (among other things).

All stocks move on news and outlook -- TA - at least insofar as chart patterns and volume/price indicators - is reflective of that. I don't personally use Fibonacci because I agree that it looks like numerology - but I haven't looked into a great deal so am perhaps wrong. However, I think there is strong utility in volume/price indicators, patterns (price movements), and support/resistance levels which are readily interpretable in terms of investor psychology and are indicative of outlook etc.

But to each their own ..