As an independent contractor, am I responsible for a flat tire I got while driving a company car during my work day?

What does your contract say about it?

As a independent contractor you should not be driving a car belonging to the company. You should be driving a car owned by "YOUR OWN" company since you are not an employee of the company.

So why do you have their car ? What is the agreement about the use?

I know that this is just my employer not wanting to pay taxes on me. I have no written contract, just a verbal agreement to use their car and equiptment for a certain amount of money per job. I'm not hourly or salary and would get more money to use my car n tools, but not enough.