Right. But it's more than that: there's no default from which to deviate in any direction. Every country can freely choose who it considers as its citizens under all circumstances regardless of which law usually applies where, and I don't think any treaties cover that (with some narrow and not-worldwide exceptions around people who would otherwise be stateless) including the ICAO ones. ICAO's rule for the "Lex loci" of airplanes is irrelevant to the nationality question except when a nation's domestic law of nationality makes it relevant for granting (or withholding) that nation's nationality.

The US nationality rule for birth outside of the US is narrower than "anyone with one US parent", by the way. It wouldn't apply to cases like mine if my time spent living in the US had been below a certain threshold. By contrast, even children born in the US to those whose presence in the US is unlawful or otherwise irregular are citizens by birth.