I think the problem here is that there are two very different meanings of "vectorized" at play. The first (and what the Julia docs are talking about here) is the pattern of writing "vector-operations" (i.e. rather than writing a loop, writing an expression that works across an entire array). The second meaning is using SIMD instructions (e.g. AVX2). What the julia docs are trying to say is unlike in languages like Python/R/Matlab where loops have a high overhead do to an interpreter, in Julia, loops are fast because the language is compiled. There are lots of algorithms that are easy to express in an iterative fashion that are pretty much impossible to vectorize efficiently (dataflow analyais/differential equations etc).

The docs here aren't trying to talk about SIMD instructions at all here. (although Julia/LLVM are pretty good at producing SIMD instructions from loops where possible).