There are always details within details. The overall idea is easily understandable. You are being pedantic.
The free subroutine deallocates a block of memory previously allocated by the malloc subsystem. Undefined results occur if the Pointer parameter is not an address that has previously been allocated by the malloc subsystem, or if the Pointer parameter has already been deallocated. If the Pointer parameter is NULL, no action occurs.
All that is guaranteed, is a deallocation. Not how and when that memory will become available again.
Your "more detailed" understanding will break, and will cause headaches, on platforms ypu're not used to.