I am suspicious as well, or perhaps stronger--I am likely to say "humbug" to such claims. Having made many of them loudly at various points in my career, starting with Structured Programming, OOP. There was also the Rational phase, as in the Rational Unified Method, in which the methodology was though to hold the true silver bullet.
Doing functional programming still leaves you with the essential complexity.
But I wonder if "procedural programming is the foundation upon which all other edifices are constructed" is necessarily true. Could we not build a computer that was truly functional throughout?