Schneider behaving badly

I was fired Friday by Schneider. The reason they give is that i falsified my application. In 2002 I was convicted for misdemeanors disturbing the peace and resisting arrest. Bogus charges, but they stuck and are in my record.
I applied to Schneider early March to work on bulk division, but failed the bulk specific physical when i lost my balance. I then went to Northeast regional with a 7 day orientation, and 2 weeks with trainer, plus 5 days extra qualifying.
First week out i have a stop at a supermarket in Yonkers, NY. After waiting 1 hour for opening to the one dock, I dock and go inside. An hour goes by nobody touches my freight. After 45 minutes i had asked if im missing something, should i unload it myself or what. They reply no, they dont have anywhere to put it, they got to make space. Finally i see some movement, but as i said at the hour mark one of their own tractor trailers comes in and after a while they order me off the dock so he can unload his freight.
I go to my truck and as i pull out i notice cars had taken up metered spaces i had used to sight side back, sight side back is not an option anymore, the other 2 trucks are going to blind side back. I was not happy, no room to hang around the area so i drove to a service plaza 15 minutes away and macroed the situation, and that i didnt want to take the risk of blind side backing on my own. The dbl( driver manager) got back to me and told me to go right back and blind side with the managers help. I figured that the other tractor trailer was done by now and went back to the store and i docked, and got unloaded then headed to the 2nd stop of the day. As i was leaving they canceled the next day's trip, and a little later sent me equipment macro to take my trailer to NJ, meaning they had already decided to fire me. Me I thought I had done my job except for voicing my concern on the qualcom, so i was suprised the next morning the dbl told me he had bad news, that they had found out I had falsified my application by not telling about my misdemeanor convictions in 2002. I knew that there was no way i had made a mistake, and after reviewing the application process i saw that as a Massachusetts resident i was directed to answer no to the question if it was a minor misdemeanor like disturbing the peace or a misdemeanor older than 5 years old. They are breaking the law and i dont know if i will pursue unemployment benefits which would be a slamdunk.
I'd rather get a job soon, but i'm asking for any advise to make sure they won't stain my DAC report and any other recourse i might have to pursue.
This is the way they operate fill up your head with all kinds of crap about safety ie: boots, seatbelts, how to crank dolly etc, but bottom line is they want you to take all kinds of risks, but if you scrach something come down on you like a ton of bricks. Like the Schneider driver who told me he had 14 violations of the 14 hour rule in the last whatever months. Can you imagine the touble he would be in if somebody ran into him at those times?
Plus the fact that the stop i had, special instructions were to ignore anybody saying that 53 foot trailers were not allowed. I'm sorry for how long this is

 

Thanks for the replies, no surprises. Of course drivers do blind side backings every day, as I mentioned. The mistake was that I voiced my concern on qualcom. Of course i did manage to make the delivery. But boom the next day I got fired, and of course they will not go near that in their explanations of why i got fired. They had to invent a reason.
I answered correctly as per directions on application form i filled out. As a Massachusetts resident (and Hawaii) I had to answer no, per the law. Its on their application. People get your heads out of the sand. This is a good law that should be adopted by more states to protect you as a worker. You are out there making 40 to $ 60,000 a year and you are voting like republicans and vilifying democrats who are trying to give give you some rights. I obey the law and Im a bad guy, while a company who breaks the law by inventing a reason instead of being afraid to be straight with you is right? If they dont have to abide by a Massachusetts law why dont they scrap it from their application?