Are you using is__writable (with 2 underscores) or just is_writable (just one underscore)?
v1.3.8 uses is__writable for the check, which actually attempts to open the file with the intent to write to it. If that attempt to open the file passes, it's reporting that the file is writable ... because it is.

If you don't believe it, that's your choice. Just turn off the warning and it won't bother you anymore.