I think you are correct. Schools could actually implement safety protocols better than the White House, if they wanted to and had the resources. Testing, tracing, masks, PPE, etc.
My boys school does Temp checks at the door, masks all day long, smaller class size with desks socially distant. Sanitation stations everywhere. For my son in Junior High they stay with their 'group' for the day. So yes, I feel like the school is safer than the WH