If your position is at a public university, you probably work at a publicly-funded building, using publicly-funded electricity and heating, and publicly-funded office material. So I'd say it should be covered.
The building I work in was built using money from two foundations. The electricity and heating, as well as office material, theoretically comes from grant indirects - which at the moment for me come entirely from private industry.
In Europe? I always thought that that sort of thing was common in the US, but it's surprising that it happens to that extent in Europe.
One would hope that 35+ percent overhead would cover rent/heating etc.