That is what my example in fact does. fun{:a,:b,:c}() is an instance of the fun{:a,:b,:c} type, which specifically has :a and :b and :c in its type, not any symbols.
julia> typeof(fun{:a,:b,:c}()) == typeof(fun{:x,:y,:z}())
false
This example shows that the types are indeed considered different if the symbols change.