Though, perhaps they meant "assemble".
A lot of other big things, like wind turbines, are shipped in smaller pieces and assembled onsite. At least according to a family member of mine who works on them, you even get slightly different designs that are specifically tailored to the local highway transport regulations in different countries.
That said, I think in general you're right that the story is that it's just cheaper to do it this way. I just think that assuming you'd need to build actual factories is a bit drastic. But perhaps even getting the equipment needed for final assembly onsite is prohibitively expensive compared to just transporting the fully-assembled equipment.