First of all the thing about hoarding being triggered by loss: I think this has more to do with psychoanalysts looking for an explanatory reason of that sort. (I.e. Freudian bullshit.) From my observation it is more of a genetic personality trait that the person has already had the inclination to hoarding independent of any life events. Certainly life events or the loss of a loved one could make a barely-in-control hoarding situation spiral out of control, but it didn't start the hoarding any more than gunshot sounds cause avalanches unless avalanche conditions were already present.
Second to the points about inability to describe the objects in detail, to handle the objects for more than a short time, or not being able to reliably tell the animals apart in an animal hoarding situation. We had 19 cats (in a 2 bedroom), and it was bad for us and the animals, but we definitely could tell them apart! Photographic memory runs in my family; most of us could in fact describe most of the objects. That's part of the problem! A tendency to see every object as unique contributes to inability to not keep them all.
I feel like TFA was written from the perspective of someone who has no personal experience or understanding. A recent experience at my mother's house provides a much better illustration of why hoarding happens. Her doorstep had rotted out and I had to rebuild it. My mother suggested I use some polyurethane coating to finish the wood, but the bottle she'd been saving had been open an unknown number of years and turned into a disgusting milkshake. I said we better not use that and would just buy a new bottle. I asked if I could take the spoiled bottle to the trash for her and she almost agreed, but at the last moment stopped me. She wanted to look up on the internet whether there was a way to turn the spoiled polyurethane back into usable, and asked me to put it in the separate RV (itself falling to pieces) until she has time to do that.
Here's the key: it's an inability to make decisions. That's it. The emotional distress component follows from the stress of being unable to make a decision, not the other way around. (The reason a decision cannot be made is because the future cannot be completely known, thus it is impossible to say a discarded item will definitely not turn out to have been needed.) The build-up of things comes from putting off the decisions to keep or get rid of things indefinitely.