what all affects THEIR insurance costs?

You never know where the info is coming from. The best thing to do is never lie on a job application and if you're hired then go for it. You'll always want to protect your records so they get and stay clean. If you were to lie and get caught your driving career would be over. Who would hire you if they read on your record that you lie on your job application? However, don't give too much information either. Just answer the question as asked.