What Rob Pike means
When you have the abstract form of an algorithm in mind, you then have to choose if you will implement it with Message Passing or Shared Memory or maybe Hybrid. You will also have to consider the type of memory access (NUMA, UMA, etc) and the Topology used (Hypercube, Torus, Ring, Mesh, Tree, etc)
This seems a lot of work to someone who just wants something, maybe even simple, done in a parallel way (e.g. parallel for).
And it is a lot of work especially if you change the topology (so you can have all of its advantages).
So you write the parallel code (be it simple or complex) and the VM or compiler will choose what seems to be the best way to go, even running it in a sequential way! (an example would be Task Parallel Library for .net)
Important EDIT:
I should mention that I am talking about concurrency in a program / algorithm and not between independent programs that run in a system.
You said that
It's well understood that concurrency is decomposition of a complex problem into smaller components. If you cannot correctly divide something into smaller parts, it's hard to solve it using concurrency
but it is wrong b/c those smaller components may depend on each other in a sequential manner to complete, so even if you divide into small components, it does not mean you achieve concurrency / parallelism.
In all my classes of parallel and distributed algorithms (both in BS and MS) we never talked about "concurrency we obtained and now let's see how to obtain parallelism". If you use the word concurrency to describe and algorithm then you imply parallelism and vice versa.
In the literature you will also find a thin line between distributed and parallel.
From an algorithmic point of view you can use concurrency, parallelism and distributed and you get the same idea.
From an implementation point of view, if you say "parallelism" you usually intend a program that runs on the local computer or a cluster (Shared Memory communication), and "distributed" when you run the program on a grid (Message Passing communication).
Now, both distributed and parallelism imply concurrency.
I think you should be more skeptical about the precise meaning of these terms because even in the literature (and I talk about people that actually contributed to this field and not just the creation of some language) they are used to express the abstract concept.
Concurrency on an algorithm (be it program) means to have pieces of code that can run independent of other pieces of code, even if they will eventually wait for some other pieces of code (check Amdahl's Law to see exactly the implication of this).
So whenever you have concurrency in an algorithm / program you also have parallelism.
I think it is better to just implement some parallel AND distributed algorithms to better understand the idea behind it. If you know C/C++ you can use OpenMPI for distributed (Message Passing) implementations and OpenMP for parallel (Shared Memory) implementations.
EDIT:
He could also mean concurrency as the abstract principle and parallel as the way it is implemented [Shared Memory, Message Passing, Hybrid between both; Type of memory acces (numa, uma, etc)].