Earlier quoted context omitted.
What should they use for password resets?
That depends on the kind of services they provide. Simplest options that come to mind are nothing (like this wesbsite) or a printed reset code with owner notification on use and 1-day wait period. At the very least they can allow power users to disable password resets when they want.
SMS confirmation is another mechanism, and one that is viable in most of the world, but has a different set of risks.
I think a combination of these are a good approach, but this is a really tough problem in the identity space, and if you have any suggestions on how to improve it in a way that is viable for a large user base, your feedback would be greatly appreciated!