#3 and this is why:
You can be the best player of the world but it can happen you loose 20 tourneys in a row. There is always a probability to lose a tourney that is greater er than zero, so there must be a probability greater than zero you lose two tournaments in a row. This is not a matter of skill, it's just plain mathematics of probabilities. This is also true if you are a winning player.
Then, if the probability of losing 2 tournaments in a row is greater than zero and losing a single tourney is greater than zero, losing three tourneys in a row must be also greater than zero. Those probabilities may get smaller, but they are greater than zero all the way. You probalby have an idea where this is going: whatever the number tourneys is, it is mathematically absolutely certain you will lose that many tourneys in a row if you play enough tourneys. The probability of it is getting smaller and smaller all the way but this means only you need to play more tourneys and it will happen some day.
Luckily there is a break on this: your lifetime is limited. If the number of losing tourney in a row is large enough you probably can't play the required number of tourneys in a lifetime if you are a winning player. (Losing players can't be saved.) This is where bankroll management kicks in: proper bankroll management diminishes the chance you lose so many tourneys that you lose your bankroll. A lot.
When you play with 100 buy ins instead of 20 your chance of losing your bankroll is way, way smaller. It is not 5 times smaller, it is more than 100 times smaller because those probabilities compound.
Your story is an uplifting one: a man got in trouble and expended all but the last bullet, but he turned the the tables and got out with merely a scratch. But you shouldn't get that deep into trouble in the first place. If you play with a proper BRM you may get a scatch here and there but you will last very much longer. Tourney play is much about preserving your chips with calculated risk. BRM is just the same only on a higher level. Do it. Pass on those nerve-wrecking going broke experiences. You won't miss them.