Broadcasting over binary functions

I'm a bit confused by the broadcasting behaviour outlined below. Admittedly, I don't understand the broadcasting machinery, but shouldn't all of these examples (ideally) return Fill objects?

julia> using FillArrays

julia> f(x) = x
f (generic function with 1 method)

julia> g(x, y) = x
g (generic function with 1 method)

julia> f.(Fill(1, 2))   # good
2-element Fill{Int64,1,Tuple{Base.OneTo{Int64}}}:
 1
 1

julia> g.(Fill(1, 2), 3)   # ok
2-element Fill{Int64,1,Tuple{Base.OneTo{Int64}}}:
 1
 1

julia> g.(Fill(1, 2), "a")   # why not a Fill output?
2-element Array{Int64,1}:
 1
 1

julia> g.(Fill(1, 2), Ref(2))
2-element Array{Int64,1}:
 1
 1

No file or test entry point is named. Start by reproducing the four Julia REPL examples with FillArrays, then trace the broadcasting machinery to compare why the scalar, string, and Ref cases produce Array results; done means the intended cases consistently return Fill objects or the behavior is clearly documented.