That first one was a ‘no one won so it’s up to the House and Senate’ scenario, not a ‘popular vote winner didn’t get the electoral college and his opponent did’ scenario. It was also at the time viewed as going pretty smoothly. Henry Clay had third place and thus was eligable to be picked, and he had a ton of influence in the House as he was Speaker and probably could have gotten himself picked, but he didn’t do that and instead backed John Quincy Adams who he was closer to than Jackson. That’s kind of how it’s supposed to go, the third place guy and the second place guy had a lot more in common than the first place guy so did a proto-coalition.