That post from Tim was a good post. But I feel he is still dodging the elephant in the room.
Your feelings are wrong. He stated what any person who knows anything about science will state.
When we observe galaxy closers colliding, see that their ICM is split into 2 components then their ICM has 2 components.
If one ICM component does not emit light and gravitates then that is dark matter.
Claiming the things we can't observe as empirically proven is getting things totally backwards.
And that is where you really go wrong - we have
observed dark matter.
The ignorance of claiming that only things that emit light can be observed should be obvious to you.
In fact the bullet cluster seems to be a special event,
Wrong
You really need to learn to read:
Simulating the Bullet Cluster
We present high resolution N-body/smoothed particle hydrodynamics (SPH) simulations of the interacting cluster 1E0657-56. The main and the subcluster are modelled using extended cuspy Λcold dark matter (ΛCDM) dark matter haloes and isothermal β-profiles for the collisional component. The hot gas is initially in hydrostatic equilibrium inside the global potential of the clusters. We investigate the X-ray morphology and derive the most likely impact parameters, mass ratios and initial relative velocities. We find that the observed displacement between the X-ray peaks and the associated mass distribution, the morphology of the bow shock, the surface brightness and projected temperature profiles across the shock discontinuity can be well reproduced by offset 6:1 encounters where the subcluster has initial velocity (in the rest frame of the main cluster) 2.3 times the virial velocity of the main cluster dark matter halo. A model with the same mass ratio and lower velocity (1.5 times the main cluster virial velocity) matches quite well most of the observations. However, it does not reproduce the relative surface brightness between the bullet and the main cluster. Dynamical friction strongly affects the kinematics of the subcluster so that the low-velocity bullet is actually bound to the main system at the end of the simulation. We find that a relatively high concentration (c = 6) of the main cluster dark matter halo is necessary in order to prevent the disruption of the associated X-ray peak. For a selected subsample of runs we perform a detailed three-dimensional analysis following the past, present and future evolution of the interacting systems. In particular, we investigate the kinematics of the gas and dark matter components as well as the changes in the density profiles and the motion of the system in the LX-T diagram.
Look at all that dark matter , Zeuzzz

!
The very existence of the Bullet cluster data is not proof of dark matter or LCDM, in fact the data is against the predictions of LCDM until much lower in-fall velocities for 2Vr200 are observed.
It is the
distribution of mass in the Bullet custer that is the direct empirical "proof" of drak matter.
P.S. A semantic agreement that we have is that the authors should not have the word proof in the title of their paper - it should be something like "Direct Empirical Evidence of the Existence of Dark Matter to add to The Existing Strong Evidence of Dark Matter".
The likelihood of finding the Bullet cluster is 100% because we have found it!
It is a rare situation, e.g. if we went looking for another such system the likelihood is ~10
-7 according to the paper's introduction. So there around 10 more bullet culsters that may be out there (100 billion galaxies, ~1000 per cluster for ease of arithmetic).
Your 10
-10 figure does not seem to appear in the paper.