Any wire can ground anywhere, hell I have my radio and gauges all going to 1 ground in the car..
It sounds to me like you dont have a large enough fuse for the fan(s), and its drawing too much current popping the fuse.
Also you don't HAVE to have a relay, it is suggested but not needed.
What size fan(s) and what size fuse are you running? You should have 1 fuse per fan.