Is the wood dryrotting, or rotting from moisture? If it's a moisture
problem, I'm with Roger Taylor on this -- the source of the moisture
that causes the rotting needs to be established. There are plenty of
ways wood can be getting/staying wet, and it doesn't matter how
something is finished.

If it's from dryrot, then they're not maintaining the siding properly.
You say they do one coat, but how often do they do it?

The stuff, to me looks like just like paint, but my understanding is that, because it is classified as a stain, only one coat of the stuff needs to be applied, and without any primer.

Yes, it looks like paint but it soaks in instead of creating a film on
the surface. And since it soaks in, no primer is used/needed.

But, just because it's stain doesn't mean only one coat. There have
been plenty of times when I've had to do 2 coats [mainly due to poor
maintenance habits of the owner]. It all depends on the siding --
condition of the wood will tell you whether one coat is sufficient.