In any program?

Direct arm work in "Waterbury Method" article:
Skull Crushers
Triceps Pressdown
Standing Barbell Curls
Standing Hammer Curls

"Hybrid Hypertrophy": Triceps work

"Art of Waterbury":
Triceps Pressdowns or French Presses
Standing Hammer Curls
Skull Crushers or Lying DB Triceps Extensions

"Total Body Training": Allows 2 sets of "assistance exercises"

This per the schedules as Waterbury designed them. Obviously you could study the parameters and take these out, but there seems usually to be a "method" to his madness so it is probably better to do the programs as he outlines.

This is the danger of taking comments out of context. Waterbury said that everyone knows who has been around the gym for a while that the best arm growth is achieved though heavy compound pulling and pushing exercises (paraphrase).

He didn't include any direct arm work in "Anti Bodybuilding" for instance. The program was designed without it. And yet not all his programs are without direct arm work. Seems it depends on other variables.

You'd have to ask him why this is. I didn't read all of his articles. I'm sure he includes triceps work to increase strength on pressing. Perhaps he likes biceps work sometimes to increase strength on pulling.

Whether he includes them or not seems to be dependant on the specific program.

I agree that direct arm work leads to bigger arms in a properly designed program of heavy pressing and pulling.

But, and this is just an example, biceps strength is a LIMITING factor in pulling exercises. No matter what you do you can't do a pull-up or a pull-down without bending your arms. If you're like me, you can't bend your arms without your biceps. Period. Any trick in the book is not gonna eliminate the fact that getting a full contraction in the lats during pulling is dependant on the strength of the relatively smaller and weaker biceps.

This just may be why Waterbury sometimes includes direct arm work depending on how advanced the routine is.

It is possible for some that while their arms are getting bigger doing heavy pushing and pulling their chest and back, for example, are suffering.

I do agree, however, with the general statement about arm growth being made here. I just believe there is a time and a place for everything which depends of the individual and the program itself.