Many class C's do have limited payload. I don't think any in the years you're looking at would come from the factory overloaded, though that was not unheard of in some old RVs. Very generally speaking, class A's will usually have more payload than class C's, though of course there's a lot of variation among specific models.
I suspect you'll find that most cases of blowouts are not caused by overloading so as much as by excessive age, by damage due to grossly improper care (i.e. underinflation), or by road hazards that could affect any tires.
My own experience with non-name-brand tires has been somewhat mixed. I did have one tire die due to tread separation, though it technically did not blow (it stayed inflated). I can't say whether the failure was due to some manufacturing defect in the tire or due to some tire damage I wasn't entirely aware of. I had driven with it over some pretty rough roads through Alaska.
I tend to be of the opinion that any tire that is DOT approved is generally safe to use within its ratings, regardless of brand. I also have not made much study of the matter.