On the other hand, I and literally everyone I know would have probably left the store with a crying kid and some slight embarrassment had one of ours actually gotten hurt. Lawsuits would be not be something coming to mind. In that light, is it not rude to treat someone the same as some of the least reasonable worst-case 'unable-to-parent-without-a-store-policy' types of people in society?

I'm not entirely sure, but an immediate jump to compliance solely to allow an employee to save face may not be a good position to promote.

I think people change their minds when they're faced with a ridiculous hospital bill for treating the injury. Their insurance pays the hospital bill and then sues the store for the amount paid. The parent isn't even really the one suing; it's their insurance company.

That being said, it's not so terrible for the parent to push back a little. The company reduced their liability with the warning. Having the parent acknowledge the risk is a success for the employee.