No tickets, will accidents show on record?

New to the forum, looking for some insight on driving records.
I have a non CDL class C.I worked for a contractor to FedEx ground until 9 months ago when I got hurt and required surgery.
Meanwhile, FedEx booted me from their system and upon being cleared to return to work they required me to go through the background checks as if I were a new hire. Last year while I was still working, I had two very minor accidents, on one of them the police did come but didn't ticket me. The other, the police were not even called.
Unfortunately, these accidents disqualified me from returning to FedEx even though they didn't result in my disqualification at the time of the accidents.
My question is, did these accidents show up in my consumer report background check just because they occurred while working for the company who requested the check? Or will these show up on any background check? I'm worried because now I'm out of work and looking for a new driving job. Also considering going to CDL school. I don't want to waste time and money if I can avoid it. I was under the impression that if I wasn't ticketed, it won't be on my record.

 

Basically 3 accidents will DQ a current employee and 2 within 36 months will DQ a new hire which is how they were considering me after my absence.
I'm thinking I should go get a dmv report to see whats on there. I'm curious though, is there a difference between the dmv report and what the consumer background check dug up? I'm thinking it has something to do with it being reported to their insurance.

If i had one more while i was still working it would have disqualified me. Since they were treating me like a new hire it was enough to disqualify me.
I'm just wondering if their background check is going off my dmv report or did they both show up because of insurance being involved. I think I'm going to go get a copy of my dmv report to see whats on there. I'm just worried that even if its not on my report, that it will still show up if a new company does a thorough comsumer reporting company background check like Fedex did.