This argument is a claim that carnists don't actually pay for chicks to be thrown into a shredder, they are just paying someone for eggs and the fact that they are being thrown into a shredder is just a thing that happens. Another form of the same argument is "I'm not paying for baby chicks to be shredded, the farmer is".
We've established that if you're doing something immoral, it's immoral to pay to have it done. Well, the same argument applies here, just simply one more step. If it's immoral to pay to have something done, it's also immoral to pay someone to then pay someone else to have something done. The fact that you go through an additional middleman doesn't suddenly justify the action. This attempt to move things one more level out is just skirting responsibility.
It's unethical to murder someone. It's unethical to pay a hitman to murder someone. How does it suddenly become justified if we and some other would-be murderers get together, pool our money, and hire a few hitmen to kill a few people? Does that absolve the crime? Of course not.
And therefore all of the same problems apply.