The site was not very  intuitive for me, maybe you will have better luck. 
"No Assembly" Yes, that is what I want. I do not want to have to assemble my filing cabinet, so I click the no assembly button and purchase my item. 
Or
I can click "Assembly $56.99" and pay less, but that is not worth it to me. So again, I click "No Assembly"... as in no assembly required. Not, "Not assembled"
According to the dictionary, assemble means "to fit together the parts of". No is defined as "used as a function word to express the negative of an alternative choice or possibility". No used in front on the word assemble (assembly) would mean to express the negative of an alternative choice. I can either assemble a product or NOt assemble a product. 

I will update this review after I spend my afternoon assembling (*Cough, I mean no assembly(ing) my cabinet.) to include if the product itself is worth while.