IANAM, but I thought really if there was one great lesson of 20th-century mathematics, it's that nothing (ie, no system of axioms) is fundamental and superior to all others. For instance, Church-Turing equivalence does not tell you that Church's model of computing is more fundamental than Turing's or vice versa.
If you look at where lambda comes from, it comes out of this same project of metamathematics that originates in the 19th century with people like Frege - how do you describe math in terms of math? Then it was discovered that this project could be repurposed as a definition of computing. Reusing old standards is a thing that happens, but sometimes you'd come up with a different approach if you were starting from scratch. As I've pointed out elsewhere on this thread, the shared theoretical foundation of lambda does not lead to a family of languages that are compatible in any meaningful sense.
It was probably a bad decision to make 0 true and 1 false, but not for mathematical reasons. There is always a lot of C coupled to Urbit, and what ends up happening is that the easiest way to handle this problem is to write C in a sort of dialect in which 0 is true and 1 is false. This is slightly cumbersome, and the perceived elegance of 0 == true isn't at all worth it. However, it's also nowhere near awful enough to revisit the question, which would be quite tricky considering the self-compiling nature of the system!