Current goes where it's demanded. IF he was grounding his fuel pump, EFI, lights, winch, etc. to the radiator I'd agree their could be a problem.
The radiator, radiator support, and for that matter the entire engine block are all part of the vehicle's ground path. If you put a multimeter on the radiator or support to check voltage you ought to see a value pretty close to battery voltage (positive lead on battery positive, negative lead touching exposed metal on the rad or support). Alternatively, checking resistance between the battery's negative lead and exposed metal on the rad or support should give you a nice low resistance level. Both of these must be true for the horns to work.