Interesting thread. So, the main reason for using clamps instead of nails is that you don't have to mess with filling all the tiny holes from the countersunk nails? 
I don't think anyone is meaning to say that at all. As in ... filling the holes doesn't count at all, one way or another.

Glue joints are what you want for mdf. No screw or nail made will provide a good solid joint in mdf, its not the screw thats the problem, its the mdf. As someone said they have made a screw for mdf thats only just lousy rather than totally crappy, it still has no strength. The way it gets a little better is that the threads are farther apart giving a little more of the mdf between the threads. imo it still sucks and certainly is not "new".
If you have ever had one of those particle board pieces of furniture I would be very surprised if it didn't have a problem at a screw joint unless you glued the whole thing anyway. That is what I am referring to with mdf. The technical reason is very simple, there are no "long" fibers in mdf. Think of it like cement without rebar. But mdf has good sound characteristics for building speakers with the added benefit that its inexpensive.
So you need at least two, flat, somewhat porous surfaces to mate with glue for a strong joint. The glue actually sinks into the mdf a little ways, and after curing the mdf doesnt really know where the joint was at all. Its strong because any load, pressure, shear whatever you want to call it is so spread out no one part of the mdf is any weaker than any other. I know of some folks that actually predampen the mdf before glueing so the glue sinks in a little further. There is nothing wrong with damp washing the fine dust off anyway! Thats another way to do the same thing richidoo is saying about letting it soak in.
But what you can achieve is that all the mdf, joint included, has the same strength. Once you have everything all put together, sanded, corners shaped or whatever you want to do, I recommend you then put sanding sealer or something similar all over every surface of the bare mdf. That will do two things, harden the surface a bit more so it will take the finish better, and it will provide a moisture barrier.
The part express article does not disagree with what I am saying, but they show you how you might use nails or screws to make sure everything fits. And not spend a lot of money on clamps. I made the assumption from the question that this was for a completely novice woodworker. The parts express article is allowing for the most common problem I too have encountered, is that things don't fit the way you want them to, and you don't notice until the glue is wet.
PE is showing how to use screws or nails to make sure it all goes together dry, but they still describe gluing it all. I did not mention their preference for gorilla glue over carpenters glue, all I can assume is that they have talked to enough new builders to warrant that preference. However ... Most people in this forum including myself prefer carpenters glue but either will work fine. If you wonder about yellow vs white glue, yellow was made for woodworking especially and is a little bit more moisture tolerant. Otherwise its generally considered the same.
Polyurethene glue(Gorilla) does have one negative attribute. Its quite a bit more expensive and the joint won't be any better when you are done. I myself think yellow glue is easier to clean up. Beware that Gorilla glue has its own problems for you to deal with, you really must practice glue some scrap with it so you learn how much to use. It expands a lot more than you would expect it to, and it takes time for it to expand completely.
So to be clear when I say yellow glue or carpenters glue I mean yellow glue, white glue, aliphatic resin, and pva.
The glue joint will last and be strong if you are careful to do it properly. How you hold the pieces till it dries doesn't really matter, you can take the nails and screws all out after the glue dries annd it won't make any difference. The important thing I think is recognize mdf for what it is and work with it accordingly. Theres many articles scientific and otherwise discussing the structural qualities of almost every material you can think of including mdf. Or you also have a bunch of opinions from a variety of people with experience trying to help out here. Thats whats nice about Dannys forum lots of experience here.
Brian