The "claim to fame" has more to do with homoiconicity, ie. that the language is its own syntax tree. This allows you to extend the language in arbitrarily complex ways in the language itself - a consequence of this is the simplicity of writing a self-interpreter.

Languages involve a lot of apparent mystification, in part because the syntax tree and the semantics of the syntax tree are not the program you are writing. Who knows what "class X {}" actually does to the (virtual) machine?

By essentially providing a 1:1 correspondence between the "real" semantics and the "apparent" semantics, programming this way can seem magical compared to other languages.

With assembly you arent taking objects of the language and making them objects of a metalanguage, ie. you arent preserving semantics when you abstract. All you're doing is creating hacks on top of the basic semantics, so in effect, introducing a new language (of specialized jumps, etc.).