Yours cannot be the correct reading. The basic C11 requirement for multi-threaded programs is in §126.96.36.199/4: "Two expression evaluations conflict if one of them modifies a memory location and the other one reads or modifies the same memory location." In this normative provision, "memory location" cannot possibly mean anything other than the internal representation of a built-in type (char, int, or other integer, or a pointer), otherwise writing multi-threaded programs would be impossible. The POSIX standard for pthreads imposes a similar requirement on the implementation.
Note that marking a struct or a field of a struct volatile is irrelevant to all this. This (§188.8.131.52) is a part of the C specification relating to access to an object of a given built-in type by multiple threads within a single process. Volatile is concerned only with asynchronous access to a given memory location by a single thread in a single process (for example, by an interrupt). Of course, if volatile were to work at all in the usage in the kernel, some prior cache synchronization would be required so approximating to what is wanted here. But even so, the compiler is not obliged to provide the behavior demanded by the kernel code in question.