As the article indicates, it may take up to 6 months for the SSA and financial institutions to get the info on deceased individuals to be able to prevent fraud/identity theft, so I'd tread lightly with recently deceased individuals. But for individuals born in 1869 and even many years later, I don't think we should have much concern.
I'm much more concerned about fraud/identity theft using SSNs of living individuals. But that's a whole different discussion that's not appropriate in this forum anyway, since we don't disclose publicly information about living individuals here.