Here is another possibility/scenario that could cause a problem like this:
If this particular website is a subdirectory website in a folder below the root of the hosting account root folder and an .htaccess file exists in the root folder of the hosting account then the security rules in the hosting account root .htaccess file will be applied to all subdirectory websites, unless a subdirectory site has its own .htaccess rules. See the forum topic link below for a full explanation of how .htaccess files work in general and in hosting environments with multiple websites installed.