Why is VS2013 complaining about “using uninitialized memory”?

Question

I have a code that goes like this:

#include <stdio.h>
#include <stdlib.h>

typedef struct {
    char *a;
    char *b;
    int c;
} my_type;

void free_my_type(my_type *p) {
    if (p) {
        if (p->a) free(p->a);  // line 12
        if (p->b) free(p->b);  // line 13
        free(p);
    }
}

int main(void) {
    my_type *p = malloc(sizeof(*p));

    p->a = malloc(10);
    p->b = malloc(10);
    p->c = 10;

    free_my_type(p);

    return 0;
}

VS's Code Analysis is complaining that I am:

"C6001 Using uninitialized memory '*p'"

        '*p' is not initialized                             12
        Skip this branch, (assume 'p->b' is false)          13
        '*p' is used, but may not have been initialized     13

I mean, it's a pointer and I'm checking to see if it is NULL . How will I ever know if *p is initialized?

Oddly enough, if there's only 1 other pointer inside the struct -- only char *a , for example -- the warning doesn't trigger. It also doesn't show up if I do free(p->b) before free(p->a) (swap lines 12 and 13).