Is it the responsibility of the web client or server to use the directory index file for the home page?

Question

The Cengage Learning textbook New Perspectives on Microsoft Office 2013 says this on page IB5:

If a URL does not include a filename, many web browsers will load the file that contains the website's home page—for example, index.htm or default.aspx.

This implies it is the client's responsibility to explicitly look for index.html.

However, from my knowledge (and this question), this is not the case. The server serves the index.html file or whatever configured file, may it be index.php, default.aspx.

Is there ever a case where the client has to explicitly ask for the "index" file of a directory? Has it ever occurred in history?

_{I'm not sure where else to ask this question, if not here.}