They are responsible for it.
However, here's a different situation:
If the company you're working for requires you to use LLMs to code, I think it's 100% defensible to say "Oh, the AI did that" when there's a problem because the company required its usage. You would have done it better if the company hadn't forced you to cut corners.
I assume (hope to god) you're being hyperbolic, but I feel it important to point out to everyone who doesn't get it. This is just the CS version of "just following orders". And deserves the exact same amount of respect and fairness.
Cleaning up after AI can easily take longer than it takes to just it right the first time myself.
I'm not saying that this is going to be a daily occurrence, and I do find that AI is great at speeding up some tasks. But it absolutely will cause errors. If they expect it to save time, they're going to have to accept an increased error rate.
Especially of hard-to-find/predict/test bugs.
If they don't require it, and I use it to lower my workload, then it's on me, not them.