No that is not quite true. The high current in the cables generates strong magnetic fields, which is what causes and why I mentioned the cables "dancing around." A magnetic field, for example, is what causes a traditional type "clamp on" ammeter to operate, what we used to call an 'amprobe'. The magnetic field(s) generated by the current in the welding cables is nothing to sneeze at.
If you want to "see" this sometime, and if you have a good 200 or more amp DC welder, coil one of the cables up somewhat, and strike a big heavy current arc. The cables will MOVE!!
The transformer field is actually quite contained, by some measure. This is simply because the conductors are wrapped around the core, and the core poles are (such as E core) form what you might call a magnetic circuit. Something that is much better is a toroidal core (a doughnut core) These, used primarily for higher frequency transformers such as switch mode power supplies, computer supplies, just about any "wall wort" of late have very very little magnetic leakage because of the construction of the core
Arc gouging at 400A
