You're right. I searched the C99 for "recurs" and found the relevant section that briefly mentions recursive function calls.
That means static allocation is insufficient for an implementation of automatic variables in a conformant C compiler. Nevertheless I still like to think of it as a valid implementation sometimes. In contemporary practice many stack variables are basically global variables, in the sense that they are valid during most of the program. And they are degraded to stack variables only as a by-product of a (technically, unnessary) splitting of the program into very fine-grained function calls.
That means static allocation is insufficient for an implementation of automatic variables in a conformant C compiler. Nevertheless I still like to think of it as a valid implementation sometimes. In contemporary practice many stack variables are basically global variables, in the sense that they are valid during most of the program. And they are degraded to stack variables only as a by-product of a (technically, unnessary) splitting of the program into very fine-grained function calls.