I don't think that HC comment re "troubled" pets is in anyways offensive nor in anyways false.
the rescue organisations get pets from all backgrounds, some are dumped because they are no longer wanted, others are dumped because they have some issues (age, behaviour, health), others are "released" to the shelter because the owner is unable to keep it.
i am not justifying the "reasons" behind dumping, i am just stating a few facts.
having worked at a few shelters, one has a little less rosy view of the reality here.
and in honesty, as stated by some of those who have adopted pets, most the dogs that are then put up for adoption/re-homing have very little in the way of issues.
interpret that as you deem fit.