You can download a Gedcom of your own tree(s), but not anyone elses even if you're invited to it as an editor.

view your tree.
there is a "Tree Pages" pulldown menu next to your tree name.
click on "Tree Settings" in that menu.
that should put you on the "Tree Info" page of the Tree Settings.
there is a green "Export Tree" button on the right side of the page.
Click it, it readies the file, then changes to say "Download your Gedcom file", then you click that.