Lighttpd

In 'Known Limitations' section of mod_deflate documentation, it says:

'mod_deflate deflate.cache-dir, if set, contains cached output of static files,
but does not cache dynamic responses unless the response contains an ETag
response header.'

As far as I understand from that quote, if a dynamic response, such as a PHP
script (I know it's your favorite language!) has an ETag header then the
compressed content will be cached, right?

I created a simple script like this:

<?php
header("ETag: some-gibberish-here");
echo phpinfo();

Below is my deflate settings:

# lighttpd has write permission, I know because static file caching works
deflate.cache-dir = "/path/to/cache/dir/compressed" 
deflate.mimetypes = ( "application/javascript", "text/css", "text/html", "text/plain" )
deflate.allowed-encodings = ( "gzip", "deflate" )

But mod_deflate does not cache that response according to the documentation.
Actually I don't expect this to work. After all, all PHP requests are sent to
the fpm backend. It's not possible to send the cached compressed content to the client
before mod_fastcgi, right?

Probably, it's something I misunderstand but could you please clarify that
quote?

Thanks in advance.