[oddevan]

I imagine there's a difference between "managed hosting" (host handles OS/package updates and maintains your LAMP stack) and "managed WordPress hosting" (host handles all of the above AND core WordPress updates, basic security, etc).

[extra88]

Dreampress's non-shared hosting plans include "Wordpress Service Updates" which surely includes core Wordpress updates and updates to plugins they include, like Jetpack. It might also cover updating a list of the most popular plugins.

For security beyond running updated software, it includes a Wordpress-tuned web application firewall and the $24.95/month tier includes "Malware Scanning & Repair."