I work in biomedical research, and this finding has been discussed quite broadly. Most researchers don't believe it.
Exactly reproducing novel findings usually requires a significant investment into the underlying procedures, which most places will not undertake. Reproduction instead usually occurs as part of an extension of the initial findings. The complexity of biology means that the first findings are frequently not reproduced exactly the same way as the original, but this does not detract from the "direction" of the initial findings.
For example, the first finding might be that protein A promotes tumor growth by modifying protein B. An extension of these findings might be Protein A sometimes modifies protein B, and when it does tumor growth is stimulated, but it mostly does not modify protein B, it instead modifies protein C, which suppresses tumor growth. In this case, were the first results replicated? Yes, and no.
You're wrong. What you say - that we conclude anything if not everything was taken into consideration - is undoubtedly true for mathematical meaning of "conclude". Mathematicians, computer scientists and a few others, like theoretic physicists, have a luxury of using law of excluded middle, which Sherlock Holmes also used. The famous detective states that if you eliminate everything that is impossible, whatever remains is true, even if it sounds improbable.
All the people who use this law do so because their work is about some kind of model, which can be wholly known. However, if you have a misfortune of working in the real world - like nearly everyone - then you can't apply this law. This means that you won't ever get a proof in a mathematical sense. You won't ever be completely certain - you can be convinced beyond reasonable doubt, but that's all.
So when we talk about how biologists are just grant hunters because someone couldn't reproduce their experiments we need to take this into account. I don't know, but if I had to guess I'd say that nobody ever expected these experiments to be 100% accurate, 100% reproducible or 100% true. I think they are treated as a data point, some input to think of, and not definite truth.
There's 20,000 broad classes of variables (genes), and on average 12 variations of each of those variable (alternative splicing, post-translational modification, cellular localization, other variables we haven't yet discovered ). This series of two experiments and likely 2 years found associations between three proteins, which is a hook into system of great complexity, a way to start looking for more.
It is not "reproducible" yet it is incredibly valuable.
Yes and no is acceptable. It's really a "Yes, but...". Is Newtonian physics correct? Yes and no. It's roughly correct at a macroscopic level, but at small scales quantum effects are important and at high speeds relativistic effects are important. "It's correct, but..."
Not every work of science needs to be exact fact before being published. Really, nothing in science is accepted as absolute fact. The scientific publishing process is a conversation between scientists to try to determine the truth.
It is exactly as you suggest, additional variables. Bear in mind that a single human cell has ~25,000 genes, and therefore at least that many potential degrees of freedom, even before you include external variables. It is very difficult to control for all of them.