Kat, the 6.0 has the same indication of black soot in the coolant reservoir if a head gasket is leaking. Also, have them look around the reservoir cap and below to see if any stains are present from coolant being forced out. If not, Does the white smoke kinda smell " taste sweet "? I'd bet the EGR cooler is to blame.
If they decide to go the fuel problem direction, and they pull the injectors, have them slide a fairly tight fitting rubber hose on the end of the injector and apply vaccum by way of a hand pump with guage. If the injector is leaking, the guage will show it.
I've got a strange " to me " smoking 6.0 here at the moment, starts and runs fine for a few seconds then smokes and all but locks up. Come to find out the head was cracked at the cups and oring and filling the cylinder full of fuel.. ouch.
Good luck, those distant troubleshoots are hard.