"anyone who supported Eddie"... oh, you mean Edward Snowden. The person who lifted the veil on the NSA snooping everyone's emails. Since when do those who support "Eddie" want everyone's emails to be transparent? We want more government activity to be transparent, yes, within reasonable operational parameters. But we, and "Eddie", want email in general to be private. We, and "Eddie", want citizens to retain their Fourth Amendment right to privacy, without being snooped by our own government for no reason.
It does seem a little weird to run one's own private email server in order to conduct state business. But as long as emails are sent in the clear between her and other people around the country and the world, then the communications are not secure, regardless of their origin. Security is only as good as the security of the weakest link in the chain of email hops, and admins on any of the hops have access to the content of the email messages anyway.
The bottom line to me, is that everyone should be using email encryption as a matter of course, and our government officials should definitely be doing that, especially ones as highly placed as the Secretary of State. Until that becomes the norm, all this hand-waving about email security is, I repeat, laughable.