Of course deductions carry scientific weight, but they don't serve as meaningful evidence and instead as the basis of a hypothesis. The very nature of an axiom in science is that of a logically-unproven premise that, itself, can't be used to scientifically "prove" a concept. Therefore, it's necessary that induction be used to justify a deduction, but any logician will assert/concede/stand-completely-baffled-at-any-counter-assertion that inductive evidence could ever be used to logically prove a deduction. Therefore, the level of "proof" for science, which is to say the level at which it becomes warranted to treat a theory as an axiom, is much less rigorous than the level at which it becomes warranted to treat a deduction as a premise. The assertion that you have to meaningfully "trust" evidence runs counter to the foundations of science is a bit of a misnomer, therefore, as one need not assume that a theory is indefatigably true to build off of it, but to assume that the theory has logical conclusions that can be tested.
I'm certainly not pretending that people were suddenly convinced because of Sputnik that the Earth was round. There were myriad reliable indicators to show us that the Earth is round (horizons, sailing in a straight line around it, high-atmosphere observable curvature, shadows on the moon, etc.), but throwing something into space and watching it circle around several times is something like the final nail in a coffin that had been comfortably nailed shut for some time. This, therefore, is why I chose the analogy of Sputnik to illustrate that stronger support for an already completely uncontentious theory is not the "proof" the article is asserting it is, it's just more strong evidence that agrees with the already-existing strong evidence.