CR64, I would be VERY leery of JB Hunt if I was you.
According to what you wrote, you've been involved in 6 incidents (total) in 2 years with 3 of them preventable. Three preventables in 2 years is alot of accidents as far as the insurance companies are concerned. Depending on the (claimed) damage, I don't think that JB will accept you, so watch out for what this recruiter is telling you.
If I was you, I would call JB's corporate offices and ask for the safety idiots... oops, I mean the Safety Dept and speak to someone there.
Or look around on the site here and find Sheepdancer's email or phone number (it's on his posts) and ask him (he is a JB recruiter). He will tell you straight up if you have a shot with JB.
Remember that a recruiter's job is to get as many people to orientation as possible. They get paid for whoever makes it. The more people you get there, the better chance you have of having some of your recruits making it through orientation.
Once you are there it is up to Safety, Medical, and the investigators to see if you stay or go home.
Going by what I saw people disqualified for at JB's orientation, unless things have changed, I would say that you will get sent home.
I won't even get into what I went through with JB over an accident I had in my own car on my time -- and I already was working for them!!!
Good Luck!