As far as my experience has been, you always need a minimal installation of Oracle connectivity, such as Oracle Provider for .Net (I believe for 9i it was still called OLE DB for Oracle), on the machine from which the connection will be made.
You don't need any Oracle Client software, just the minimal provider libraries.
Ultimately, any connection to Oracle needs to find a tnsnames file on the client machine to resolve the database name.
However, if your client is connecting to a Web Server or such and the Web Server is the one to connect to Oracle, then only the Web Server needs the Oracle connection drivers. It will send the data back to the client, but the client is not actually connecting to Oracle directly.
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