There is no such thing as "permission to the mapping" - you can only MAP_SHARED or MAP_PRIVATE - in the latter case the updates are not visible to other processes mapping the same file. Whether you can mmap() a file solely depends on permissions of the file - the one you pass in to mmap using the "int fd" parameter. So if two processes both have READ access to a file, both can mmap with PROT_READ and if both can madvise() then the kernel zaps the page ranges.
Do you see anything in the Linux kernel code that says otherwise?
MAP_SHARED and MAP_PRIVATE are indeed permissions (not particularly fine-grained) to the mapping. Perhaps they don't come into play here, but saying "there is no such thing as 'permission to the mapping'" is false.
I really doubt that if two processes are mapping the same file, and one calls madvise(MADV_DONTNEED), it'll drop the pages from memory entirely. That seems like a great way to let one process DoS another. If the other process has marked it MADV_WILLNEED, that would be especially bad.
If they've both mapped it MAP_PRIVATE, then the mappings should be entirely separate anyway (though copy-on-write semantics are presumably used), and a madvise() on one shouldn't affect the other.
Do you see anything in the Linux kernel code that says otherwise?