Sleeping doesn't restore health in hardcoe mode, only in Casual mode.
To restore HP, and limb CND, in hardcoe mode via sleeping in a bed it must be owned by the player identified as "My bed". Safe house beds, your Novac room, beds in the lucky 38 and such ilk are good examples.
The Wiki is hardly authoritative on this subject. giving it only one mention as a Note on the hardcoe page. It states that owned beds (including sleeping with certain NPCs) will restore the player completely as well as give the Well Rested Perk.
Kor'Ah seems to confirm this.