The core feature of generative AI is the human isn't the author of the output. Authoring something and generating something with generative AI aren't equivalent processes; you know this because if you try and get a person who's fully on board w/ generative AI to not use it, they will argue the old process isn't the same as the new process and they don't want to go back. The actual output is irrelevant; authorship is a process.
But, to your point, I think you're right: companies super think their engineers have the rights to the output they assign to them. If it wasn't clear before it's clear now: engineers shouldn't be passing off generated output as authored output. They have to have the right to assign the totality of their output to their employer (same as using MIT code or whatever), so that it ultimately belongs to them or they have a valid license to use it. If they break that agreement, they break their contract with the company.