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Your first paragraph led me to believe you were on the right track, but then you veered. :-) The problem I had with your argument was not the specific case, but that you used an invalid general claim to argue it. Let the Lefties use the fallacious arguments; let's keep ours tight. That is, certain negatives can be disproven, as you mention later (which yields my point).

You claim: ...proving human activity is not responsible for global warming is a in-practice impossible task, as you could not in one lifetime analyze every human action and derive its ultimate effects on the global temperature.

That ignores other ways that a negative can be disproven...again, via contradiction. Brute force isn't necessary. For example, if we were able to prove (absurdly and hypothetically) that all inputs to a global climate system are dampened out unless they are repeated within 1%, exactly at a frequency greater than a human lifespan, etc., then wouldn't that be proof that humans weren't forcing the system? And we did it without interrogating a single human. We can prove that Tyrannosaurus Rex did not watch TV, even without finding the electric bills of every dinosaur...by proving that the conditions for a "positive" result cannot be met.

...insufficiency of global warming theories...

Insufficiency of theories and status of provability say nothing of the truth, though....they are only measures of validity of an argument. Still, beyond it all, we make decisions with far lower standards than "proof".

...we are not arguing over Invisible Pink Unicorns here.

bbhhh :-)