You may need someone else's permission" because the Smithsonian doesn't guarantee that noone else in the world has a (good or bad) IP claim to one of the donations.
That's not the intention of CC0:
In contrast to CC’s licenses that allow copyright holders to choose from a range of permissions while retaining their copyright, CC0 empowers yet another choice altogether – the choice to opt out of copyright and database protection, and the exclusive rights automatically granted to creators – the “no rights reserved” alternative to our licenses.
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Dedicating works to the public domain is difficult if not impossible for those wanting to contribute their works for public use before applicable copyright or database protection terms expire
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CC0 helps solve this problem by giving creators a way to waive all their copyright and related rights in their works to the fullest extent allowed by law.
In this case Smithsonian seems to have done the work to make sure they are out of copyright, and now they don't reserve any rights to the work.
That's not the intention of CC0:
In contrast to CC’s licenses that allow copyright holders to choose from a range of permissions while retaining their copyright, CC0 empowers yet another choice altogether – the choice to opt out of copyright and database protection, and the exclusive rights automatically granted to creators – the “no rights reserved” alternative to our licenses. ... Dedicating works to the public domain is difficult if not impossible for those wanting to contribute their works for public use before applicable copyright or database protection terms expire ... CC0 helps solve this problem by giving creators a way to waive all their copyright and related rights in their works to the fullest extent allowed by law.
In this case Smithsonian seems to have done the work to make sure they are out of copyright, and now they don't reserve any rights to the work.
https://creativecommons.org/share-your-work/public-domain/cc...