This image tells it all: https://d262ilb51hltx0.cloudfront.net/max/953/1*QXypiHUwjJZr...
What he was saying is, if there was just 1 gram per cubic cm less mass in the original universe, then it would expand too quickly to form any complex structures and the universe as we know it would not exist. And if it was just a few grams per cubic cm more massive, then it would collapse immediately as in the original question.
The reason our universe did not immediately collapse is not a mystery. It was a tiny amount less massive than would be required for such a collapse.
The reason it was perfectly on the line is no mystery whatsoever: if it were one gram over, it would collapse, and we would not exist, and thus we would not be asking the question. Same if it were one gram less; the universe would be too sparse for life to organize.
This is not a miracle or a mystery, it's simply fact. Billions or trillions of universes might have sprung into existence over billions or trillions or perhaps even infinite aeons of time, each with different masses and parameters of physics.
The one that produced an observer was observed. That's us, and that's it. No miracle, no mystery.
It's like someone winning a lottery. The chances of a specific individual winning are next to nothing, but the chances of anyone winning are 100%. If a news crew then goes and finds the winner, they will surely find an astounded, surprised, and very lucky feeling person. But the news crew will not be surprised, since their observation is entirely expected and even guaranteed.
Humanity is both the winner and the news crew in this situation, by the simple property of our ability to observe our own existence.
This is called the anthropic principle. It also applies with zero modification to the question of why Earth appears to be such a perfect planet to support human life, especially as we begin to discover that there are literally trillions of planets in our universe. We should not be surprised that we observe the one that happened to have the conditions conducive to the evolution of a sentient observer. But you could be forgiven for feeling very lucky that you're one of them.