I'm not exactly sure how Cygwin interfaces with the windows system to have unix like permissions with chmod. I have ran into problems where Apache couldn't work with specific files and folders because of permissions, and cygwin with chmod was not able to solve the problem.
To resolve the issue with Apache, Windows Explorer was used to grant permissions to 'SYSTEM' from the outermost folder and all child folders. After this, cygwin showed permissions as r-xr-x—, and sometimes with a + on the end.