One thing that can happen when you are doing computer modeling to find the input parameters that explain your observations is getting stuck in a local maximum. I am absolutely ready to believe that eliminating dark energy from current models makes their results look less like the real universe, but the number of re-runs that would be required to sample the entire parameter space and demonstrate that there were no other parameterizations that looked like our universe would be enormous, and if you include the possibility of new theories, infinite.
There would either have to be some kind of theoretical reason to think that the best known parameterization of a simulated lambda-CDM universe is not merely a local maximum, or the parameters would have to be well-constrained, by observations, so that the free parameter space was small enough to exhaustively explore. I am not aware of either condition being true so I will express some skepticism about the conclusions from the models. Nonetheless, my lack of knowledge about those conditions is not very strong evidence for their absence, and I know there could be someone reading this and feeling very annoyed that I don't know about the Backhausen-Thule principle, or whatever piece completes this puzzle. (Your contribution to the discussion, oh annoyed reader, would be greatly appreciated.)