Sorry to hear about the damage to your camper.
Maybe I'm the only one, but I don't see where a dash cam would help you much in this situation.
You said less damage than your deductible, so less than $1000 damage? Or maybe you have a really high deductible.
Assuming you have a normal deductible, the cost is pretty small to repair. More of an aggravation than anything.
If the trucking co is blowing you off, they are banking on the fact that you don't have enough at stake to take them to court. Travel to wherever, cost, lawyer, cost etc. by the time you're done it cost more time and energy than it's worth and they know it. They likely wouldn't respond differently if you had it on video. I mean you have pics already and they are giving you the finger.
Again, it stinks you're getting the runaround , but I'm also not sure where the liability lies in a no fault deal like a blown tire either. Is it different than hitting a piece of tire laying on the road that was deposited a minute earlier, even if you see the truck with a shredded tire pulled over 2 mi later?
If it was the company I work for, they'd pay up if you ran into his truck while it was parked and just claimed it was the drivers fault he was parked there!