I was speaking probabilistically, because science only knows things with relative accuracy.
What you're describing is technically correct if you're dealing with known truth values. It's just the denying the antecedent fallacy.
However, real life is more complex than that, and it's a statistically viable argument if you don't know precisely the truth one way or the other.
In fact, the quote "absence of evidence is evidence of absence" can be proven using Bayes Theorem, as long as you interpret "evidence" as increasing the likelihood of something being true and "not-evidence" as doing nothing.
But the point is that it's just what's probably true, not what's necessarily true.
You're right in that, strictly speaking, it's a non-sequitur; but probability theory tells us "absence of evidence is evidence of absence" is right more often than not.
Yes, your albatrosses are probably extinct. It's a mathematical fact. That's all "evidence of absence" means.
I think we're on the same page here, just thinking of it from different lenses.