This is not true in general, you can add methods to anonymous functions:
julia> f = (x) -> x^2
#16 (generic function with 1 method)
julia> (::typeof(f))(x::Int) = 10x
julia> f
#16 (generic function with 2 methods) # Note that f now has 2 methods
julia> f(2.)
4.0
julia> f(2)
20