If you hire someone to print it on the shirt for you, and then distribute the shirt, you would be liable for copyright infringement, not the printer, because the printer isn't supplying the artwork, you are. It's no different than placing phone calls to perform an illegal activity. The phone provider isn't guilty, but you are.
If you order a custom shirt, and provide unlicensed copyrighted artwork, but don't distribute it, then no one is in a position to get in trouble.