Earlier quoted context omitted.
Is it a good enough reason though? That would depend on the likelihood of losing your job by refusing, the ease of finding a different job, the seriousness of the unethical request, and the likelihood of getting caught.
When asked why you were fired, being able to say "I was asked to do something illegal or unethical" is a strong response. That certainly helps with the "find a new job" part.
The only time you're allowed to mention this is when it becomes easily verifiable in something like a newspaper. I actually have personal experience in one of my jobs where the owners very casually asked me to do some unethical things and then shrugged it off. At the time I highly suspected I was fired because of it, but had no evidence. So for years at interviews when asked why I was fired, my answer was "Nepotism," which is true because they replaced me with an incompetent relative. The FTC shut them down 5 years after I was fired. I only mention it if the employer tries to verify past employment and asks why the phone number doesn't work.