After correctly describing what the --remote option does in the first paragrah, the docs give the following example

c2patool sample/image.jpg -r http://my_server/myasset.c2pa -m sample/test.json -o signed_image.jpg

In the example above, the tool will embed the URL http://my_server/myasset.c2pa in signed_image.jpg then fetch the manifest from that URL and save it to signed_image.c2pa.

(emphasis mine)

This directly contradicts the first paragraph, which says that the tool will generate the .c2pa file itself. The tool will not fetch the manifest from the remote URL. It will create it and expects you to then make it accessible at the URL that you specified.