I have a 2009 32 BHDS that I bought new Feb 2010. Have used my heater in some cold/freezing weather and have not had a problem resulting from the exhaust vent. Within 3 years I found water intrusion in the bottom left front corner of the front slide out. I saw the tips of tiny bits of corrosion in the bottom of the corner. I pulled out the sleeper sofa and cut a 18 by 14 section of the interior wall with a box cutter. Found a rotten section of the floor and lower support strut. Made the repair and sealed the area from the outside with fiber glass cloth and resin. Has worked like a charm and you don't see where I cut the interior wall because the couch hides it.
My bet is that you have water intrusion and specially if that is what Jayco thinks it is. Jayco put a entire new front on my trailer due to concealed water damage Summer of 2013. Water intrusion is the death knell for RVs.
Would like to know what you find to be the cause of your damage.