I haven't read the Nature article. However, the newspaper article had a sufficiently complete description to infer what they did to infer.How did they test for the distant ancestors not having this ability at a low level?
The scientist kept frozen samples of the distant ancestors, i.e., the bacteria that were first placed in a flask. Samples were taken from the flask about every 5000 generations. I think that comes to about one sample every 2.5 years. They could check for the ability to digest citrate in the first and subsequent samples of frozen bacteria. I think they did that, although I have to check.
The frozen sample of stock culture showed no measurable ability to digest citrate. If you doubt it, ask them for samples of the stock solution. That is the entire reason that they are storing frozen samples.
If the original samples showed the ability to digest citrate at a very low level, then it still wouldn't matter. Finding that the original bacteria have a very small ability to digest citrate would merely show that the molecules were not really "fine tuned" to begin with.
We know that anyway. Actually, none of the chemical reactions require such precision that absolutely no other reactions can happen but the one. The specific shapes strongly bias the chemical reactions to one particular chemical reaction. However, they don't restrict other chemical reactions from occurring. Many metabolic diseases come about because the precise "correct" chemical reaction doesn't occur.
Mutations occur because the fidelity of the copying process is not totally specific. Cancer often starts because copying DNA is not so specific. Our digestive systems can handle lots of artificial chemicals, although not with perfect efficiency. The specificity comes because of natural selection and time, not because anyone designed the molecules for a specific task.
The fact is that the shapes of the molecules slowly changed, generation after generation, until they were specific to an entirely different chemical reaction. Complex changes in the molecules and the timing of gene expression were necessary to get the bacteria to digest citrate efficiently. Thus, the experiment shows that "fine-tuning" is the product of "time not design".
I doubt that the original bacteria had absolutely no way to digest any citrate. Even if the scientists couldn't find any such ability in any sample of bacteria, I would still suspect that there was a low level of citrate digestion. The reason that I would suspect this is because I know that no biochemical system is 100% specific to the one chemical reaction that it is "supposed to do". However, "supposed to do" is anthromorphizing. The specificity is due to generation after generation of random variation culled by natural selection.
At the beginning of the process, none of the bacteria had any metabolic chain of reactions that was specific to citrate digesting. The metabolic pathways were specific to something else, although they were never completely specific. This means that the shape of the molecules wasn't precisely "right" for digesting citrate, though it may have been mostly specific for something else. At the end of the experiment, the bacteria had a metabolic chain of reactions that seemed specific to citrate digesting. Hence, the fine-tuning of the citrate pathway is an illusion of time.
You wouldn't dismiss the evolution of ape to man by saying that the ape has a "small ability to reason". Saying that the bacteria had a small level of ability to digest citrate is like saying that nonhuman apes have a small ability to think, or that nonhuman apes have a small ability to determine when something is wrong. Or that dogs have a small ability to socialize. Natural selection is hypothesized to take the nonhuman apes small ability to reason and make it into a human ability to reason. That is how humans became human.
Specifically, the experiment knocks "irreducible complexity" on its rear. Whatever the metabolic pathway is now that digests citrate, that metabolic pathway has segments that were useful for something entirely different. Thus, the metabolic reaction for citrate has complexity that is reducible.