Counter point, why should '/' be invalid? I'm not saying it's good practice or that the compiler shouldn't warn you, but "/home/me/path_to_thing/file" is a perfectly valid path.
An absolute path is a valid path on the filesystem. But the compiler should be searching according to its implementation dependent search paths, when doing <>. Not prepending the searchpath (and not rejecting) for absolute paths is an implementation choice I personally think is wrong for a C compiler. But it may be able to do so I guess as you can also do "..".