> if modifying b causes a read/write of a, this is wrong.
No, it's not. Believe me.
The volatile keyword doesn't say anything about when it will change value, be read/written etc. It says simply that it will not be cached in a register such that every read will get the "latest" value expected when executed under the Abstract Machine.
It says nothing about threading.
It says nothing about interrupts.
Simply remember that volatile is not magic. Think of it as the opposite of "register."