I went to school in CA from K-5 and I believed them. I thought I would be safe from a nuclear attack if I put my head under the desk and covered my ears and eyes.
Stupid, yes, but I trusted my teachers.
You would have been a lot safer from glass and 'fabric' shrapnel, no doubt about it. People always assume that they'd be in the area of the fireball with a 100% death rate - but of course the largest area affected by any explosion is around its periphery.