I doubt logic changes substantially over time. The burden of proof is not a fallacy. Saying that the other person has the burden of proof is, if true, an entirely valid statement.
If you are claiming that something is, then you do have the burden of proof, no fallacy involved.
johntitor, read the following and then ask yourself can anyone disprove the claims that nasa makes? Substitue 'probe' for 'teapot', if that helps.
Russell's teapot, sometimes called the celestial teapot or cosmic teapot, is an analogy first coined by the philosopher Bertrand Russell (1872–1970) to illustrate that the philosophic burden of proof lies upon a person making scientifically unfalsifiable claims rather than shifting the burden of proof to others, specifically in the case of religion. Russell wrote that if he claims that a teapot orbits the Sun somewhere in space between the Earth and Mars, it is nonsensical for him to expect others to believe him on the grounds that they cannot prove him wrong. Russell's teapot is still referred to in discussions concerning the existence of God.
miseros claim was fallacious: "YOU NEED TO PROVIDE EVIDENCE OF A CONSPIRACY OR IT CAN BE DISPROVEN WITHOUT EVIDENCE."
I am actually familiar with that delightful notion of a teapot (though it's a teddybear in the last account of it I'd heard). However, it's not relevant in this case, because the 'teapot' in the hypothetical was never in a position to be observed: the probe is, and is still being observed (albeit indirectly). Receiving signals observing a launch: there are many ways to have verified that it does exist.
Because you neglected to be part of any of those observations, you do rely on others' word, but that is your doing, and is nothing to do with the situation, so the hypothetical does not apply. There is evidence for the existece of the probe.
To argue against it, you have made a positive claim of a conspiracy, and the burden of proof there is on you.
In addition, what you call the burden of proof fallacy was never relevant. You made a positive claim, so you did need to provide evidence for it. That evidence could just be that you reject the claims of NASA.
However, if your only response to a teapot is to suppose another teapot, you can no longer call your view any more intellectually tenable.