My company paid a third party for all my relocation expenses and reported this in the W-2 box 1. Should they report the relocation amount paid in any other place?

I have received the 2018 W2 from my company with all my relocation expenses reported in the box 1. I understand this is correct, since they are taxable. However they have hired a third party, and not paid me directly. So a company was responsible for paying all my relocation expenses (i.e. moving household goods, transportation, etc.). Is this correct? Shouldn`t they report the specific amount paid to this third party company in another place as well, like box 12, since I have not received this value directly? This is not a reimbursement, since this company paid directly the vendors.