Get a discussion going with the shop owner, yall need to sit down and have both parties have their say. The shop owner has money out on labor and the welding, and hes gotta pay his guys, but he screwed up big time by not authorizing the work first. On your friend's side, he got side lined by a repair bill he wasnt expecting to pay, and a bill thats pretty bloated for what it is. Both parties are in a rough situation on this one, and to avoid getting lawyers involved its important that yall sit down and talk this one out. Have your friend explain the situation from his point of view, but be understanding of the shop owner's position. Saying something along the lines of "I know yall are busy and its easy for a small project to get overlooked like this, and I want to find a common ground where we both work out well" will work a lot in your favor for negotiating a proper payment, and will help keep the shop owner from locking up on you and saying just to pay the bill or get a lawyer. Ask him how much it cost him to get the bracket repaired, and print out some ebay and car part.com pages with the exact bracket for sale. Show him the costs of just getting a replacement, and I would start with an offer to pay what the welding shop charged, plus what a comparable bracket would cost shipped to the shop. Expect to be flexible with your negotiations but dont pay that full bill. Explain that your friend has been missing his truck for work and needs it back soon, and that yall are interested in quickly finding a fair price for both parties to be happy.
Its a sticky situation, but navigated correctly it shouldnt be too bad. Remember you are the customer so you have the advantage that he (should) be trying to make you happy. Good luck.