Could auto-update delete core WordPress files and cause a white screen of death?

It turns out that the problem was caused by the Plesk server admin system which had been used to install WordPress, Plesk tried to upgrade wordpress on that domain and it failed and partially deleted the contents of those folders.

Plesk enables auto update for all applications installed using its “application vault” feature. So if you’ve got this same kind of set up then make sure Plesk’s auto-update feature is switched off and let WordPress’s own auto-update feature run instead.