...The problem was that Apache MultiViews were enabled by default in GoDaddy hosting (at least in their shared hosting 2.0 environment).
Apache.org docs say the following about multiviews:
The effect of MultiViews is as follows: if the server receives a request for /some/dir/foo, if /some/dir has MultiViews enabled, and /some/dir/foo< does not exist, then the server reads the directory looking for files named foo.*, and effectively fakes up a type map which names all those files, assigning them the same media types and content-encodings it would have if the client had asked for one of them by name. It then chooses the best match to the client’s requirements.
...Just add the following to your .htaccess file in any directory which you do not want to use multiviews:
Options -MultiViews
