What are yout talking about? Your deductions are completely out of context.
The Hero stated that the Villain had been protecting his BB; this shows that the Villains range could be anything. Putting this into perspective, we must analyze the Hero's thinking. From the heroes perspective, JJ is a stong preflop hand, understandable 4x raise. Going onto the flop, that's fantastic, no flush draws outside straight draw, but the fact the Villain pushes so much should make the Hero feel uneasy. The bet on the turn was $1.50... $4.52-$0.74-$1.50= $2.28 (The Villains stack after his $1.50 bet). A raise by the Hero here would make the Villain allin. To minimize losses vs. mazimize profit, the optimum move for the Hero would be to call (which he did). The villains range consists of pretty much anything, including 2 pair or trips* (more likely than trips seeing as one would call BB to defend their lower pockets). A raise on the river would be somewhat rational. Villain probably expected the raise hoping for a three-bet.
From my original post, I stand by to defend the Hero's actions. My rationalizing is not after the result, I just anazlyzed each position so your claim is dismissed.
Maybe you are more of an aggressive thinker, but this is my thought process during this hand.
Your making some assumptions that may or may not be correct, and if they are correct don't match up with the rest of your thoughts.
1: The villain is defending his BB with any two cards. At pre-flop we do not know that is the case. He could be calling a fairly tight range. potentially not "defending," but rather had cards he wanted to see the flop with. However, if we assume that he is making this play with any two cards (I am guessing that when the OP says he is defending he means calling, not a raise) then that must inform the remainder of our decisions.
2: The flop. So we should be good a lot of the time here on the flop. We have over cards and a T is probably in a lot of this guys range. If he is calling with ATC then he could very easily have a pair here. If he does, then we should still be fine. It is a very strange line to take to donk into the PFR. If he is playing ATC at this point we should still figure that we are ahead most of the time. This guy is getting aggressive but his story doesn't make any sense. What could he have hit here? A set? two pair? Maybe, but a broad range doesn't make that likely. And a bad player is likely to over value his mediocre holdings. If we assign a tighter range to him we could think that this is a better hand. This is where your thinking kind of contradicts itself. If he is playing a broad range, we should be fine. If he is playing a tight range we should be worried. If we are concerned we are losing here then we shouldn't be thinking he is playing ATC.
3: On the turn the 8 shouldn't really change much, It makes one draw better, and now makes a pair of 8's ahead of us. Bu thats about it. So based off our pre-flop and flop reasoning we should likely be ahead. The villain leading with a pot sized bet is super spewy. We do have to reconsider his range here. What kinds of hands would we assume are doing this? There really aren't any that make sense. It is a strange line to take with any hand, especially from someone who played the pre-flop so passively. Its hard to imagine this as an over pair, given his post flop aggression its not likely he would have just called preflop. Its hard to think this is a set - though that could make sense. He just wants to jam on us with a set and hope we call his spew. It could be a pair maybe its a bad player trying with a marginal hand trying to get us to fold. Or it could be air and just trying to get folds with big bets.
Given that we have assessed his range as weak, I would favor thinking he is either over representing his hand or he is
bluffing with pure air. There is some amount of the time that he is ahead but this is just the most uncoordinated dry board. He is not check-raising us, and is just throwing money at the pot.
I would really not mind a shove on the turn. If he is ahead of us, that might be enough to get a fold - though that is unlikely from this guy. We also get calls from many many worse hands that have over committed themselves. I think that is the best play. Maybe we fold a better hand 5% of the time. I think that he is just very very likely (based off his play) to get a call from those single pair hands.
I really don't like a call here. We have already committed ourselves at that point. Is there ever a time that we call the turn that we don't call the river? I don't think there is. We have too much money in the pot and can't really fold to a
bluff. So if we are going to call that river bet we may as well shove the turn instead. It puts pressure on him to make a bad call.
It would be better to call under a very specific set of circumstances. We would have to recognize that we are calling any river bet as well. We would have to know that he will only bluff or bet with weaker hands AND that he would always check his better hands. If we don't know that he is doing that, then we should just shove.
A fold is okay too. You can fold without committing much more. I think that we are ahead a little too often for a fold to make a lot of sense but I think it is better than a call.
So I would rank it as shove, fold, call. Shoving puts pressure and gets value. Folding saves our bank roll from putting too much money in the pot with medium strength hand. Calling commits us and we have to call all value bets on the river.