I know I would. If someone gives you a choice A or B that both screw you over, there's always an option Z somewhere. It might be so outrageous they don't expect it but it's there.

However usually it isn't necessary. I've been put in situations where I had to do something unethical. I've refused. And every time that choice was respected. Only if I'd have been punished for it would I have considered more severe options.

But really if you take a hard stand and have good reasons, reality tends to bend a bit further than I expected.

And yes I know what these jobs are like. I have worked in that industry a long time. With both very good and very terrible employers.