Eligible for rehire?

Being eligible for rehire doesn’t mean your former manager would actually hire you back. It simply means does the company have any reason they wouldn’t hire you back—which is often due to termination for cause, such as criminal activity, ethics violations or general corporate policy violations. Having a fallout with a manager, who may or may not work there, isn’t what they’re looking for. Also if you were eligible for unemployment after you left (and most people are even if they quit) you would likely be eligible for rehire. This is not much more than customary due diligence to ensure you worked where you said you worked and you didn’t commit some kind of fraud that resulted in your termination.

Thing seriously about whether you want to work for a company that's going to conduct this type of inquiry. When you are looking for a new job, you've obviously left your last job, and you wouldn't have left that last job if things were hunky-dory - obviously there are REASONS why people leave and that doesn't make the person any less valid of an employee. It sounds like this new company is going to be strong-arming you from the get-go. I wouldn't pursue that opportunity.