Another reason this might happens, if you are using IIS (Internet Information Services) for Windows Servers, by default, directories under \inetpub\wwwroot are not allowed to be modified through the browser. To fix the problem you only need to add permission for IIS_IUSRS user to the WordPress Directory.
IMPORTANT
Do not apply permission to the \inextpub\wwwroot, that’s a very bad idea. Also, you can add permission only to you content only.
I would only apply Read & execute, List folder contents, Read, Write. If that do not work, apply Full Control, only if previous selections do not work.
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