You've got two problmes here, Firstly a misunderstanding of what it means for an argument to be logically fallacious and second a failure to understand the actual reasoning.
For an argument to be logically fallacious simply means that it is not valid deductive logic. That is the truth of the premises does not guarantee the truth of the conclusion. An argument that provides assurance that the conclusion is almost certainly true is logically fallacious. Since that is the most that science actually claims it isn't that important that it's methods fall short of rigourous deductive logic. (Note that "fuzzy logic" does deal with probabilities and the scientific method could well be valid under those conditions).
So science doesn't rest on pure deductive logic. How then does it work. By considering probabilities. Let us suppose that a theory predicts a certain observation that will be true if the theory is true and true with a probability p if the theory is incorrect. So you have a probability p of being wrong if you guess that the theory is right on one observation. But when you add other observations in the probability goes down. Two such predictiosn and the probability is p^2, three and it is p^3 - and probabilitis can drop pretty quickly.
Let's use an illustration. Suppose someone else is flipping a coin and it comes up heads first time. You wouldn't guess that there was anthing wrong there. Suppose that it comes up heads 10 times in a row. You might start to suspect something there - the odds are worse than 1000:1 against that happening by chance. Thirty times in a row and the odds are a billion to one. Any sensible person is going to get suspicious that there is something not quite right going on at some point in this performance. And every further head will - rightly - make them more suspicious. That's the sort of reasoning you have to address. Cumulative probabilities adding up to one whacking great improbability - not simple examples like the sort you present.
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