That's not at all what local reasoning means. Local reasoning is the property that a piece of code contains (when including the call graph) everything that can affect what it does. All mutation of a value is kept within some scope of ownership of that value. If you want to understand a piece of code, you can do it by understanding that piece of code, not the program as a whole.

Assembly makes non-local reasoning mandatory, as any code can update any location in memory without restriction. All memory accesses are global. References need not even be by name - they can be via computed addresses. There are no restrictions in place allowing the structure of the program to provide boundaries on what pieces of code may be understood as units.