Sparkasse savings bank and other state-run banks

Except they're not state run.

Sparkassen and Landesbanken (and statutory health insurers and public broadcasters) are so-called "corporations under public law": publicly chartered companies that autonomously perform a public mission. The supervisory boards (quite properly) include representatives from the appropriate level of government, but the organizations are all managed by trained professionals (in Germany, there exists a vocational qualification and a degree program especially for the Sparkassen).

The state has no role in their management.

Also, the Sparkassen are not "state" so much as "municipal" - cities and counties.

It is worth emphasizing that the reason the public-law banking sector has come through the credit crunch largely unscathed is because they have adhered to their mission of providing credit and savings opportunities to small savers and businesses, respectively general economic development in the case  of the Landesbanken. The exceptions like WestLB screwed themselves by trying to be high flyers.

The fact is that what we're experiencing right now is a top-down disaster. -Paul Krugman