I am totally opposite to your conceptions listed here, as you may speculate from my "subscript" (young earth creationist by faith and by interest). But the purpose was actually not a discussion of the evidence, but rather that maybe someone knew the reference directly to that meeting. I watched a video on youtube yesterday where the speaker related the story of this meeting also, but he did not elaborate.
It must have been this video with Francis Collins:
https://www.yout ube.com/watch?v=HaEQyNeaFZs (remove a blank space)
I agree with you that the actual reason for dating the universe to 13billion years is a convoluted projection.
The difficulty is it is based on theoretical physics and untested observations of light coming from other galaxies. The cumlative affect of all the theories taking our known laws of gravity and energy release in electro magnetic radiation, the observations where interpreted in our current solar system framework.
You will notice that the models they produced for spinning galaxies and how they should look based on the observed matter seen, they should be shaped differently. The models suggest a massive gravitational source if present would give the required shape. They call this dark matter and dark energy, which makes up 95% of everything, except it is undetectable.
You may be aware that this kind of metaphysics is religion not science. So your real question is what makes this house of cards stand up. The answer is it appears to be simplest explanation in scientific equations, so it is the one they are sticking with.
My problem with 6,000 year creation is some simple local physical affects. The milky way galaxy is about 100,000 light years across. So the most distant stars we can see sent out their light 100,000 years ago.
So in our simplest understanding the local galaxy must be much older than this. What is also ironic, is some theoretical physicists are suggesting this is all a simulation or put another way, invented to appear a particular way but actually it is just a projection.
A simple problem I came across. If you can infinitely divide an item to smaller points, you come to a limit where it is either one or the other, or else it never ends. Quantum physics seems to define this point of the end of division. I suspect in reality chaos and variety are limited, and are creations to allow exploration of the possible in a limited world God has created.
Physicists are so atheistic in their convictions, they need to invent the multi-world hypothesis, or infinite variation and dislike real limits or absolute constants that are immutable to create life. To admit immutable reality, is to admit a creation and a creator, which they hate.
A funny side proposition is distant galaxies rotate as they do because its easier to create and show, not because they really exist.
I have to laugh at Elon Musk's idea of going to Mars. We went to the moon 50 years ago, and have not got further. Apart from experimental playground, its earth and its complexity we need to focus on.
A side note that a lot of people miss, science has shown everything is 99% nothing. Everything that is looked at is made up of something smaller that is mainly a force and not solid in our macro sense of solid. So it is not a leap to suggest the framework in which we exist is not as restrained as we imagine or experience. Take light. A photon is one unit of radiation, but that's really all we know. It is all so weird when the world we live in seems so concrete and certain.....
God bless you