Libraries and museums burn down all the time, or get destroyed in wars. Consider the recent fire at the Hewlett-Packard museum, where all the paper history was lost. Nobody made a backup, even though paper lasts longer term than data on a hard drive.
Frankly, I think storing data as ASCII in pits on a substrate is a great long term solution, as it can be read with a simple optical microscope, and ASCII is forever.
One of the cool things about digital data is it can be copied forward limitlessly. Make the seed genomes public domain and put them on a server - people will make copies, like they make copies of wikipedia to store in their prepper bunkers.