The issue of "comprehension" is a boondoggle that educators use to make what they do look much more complicated than it actually is, and to justify bad curricula that don't teach comprehension or rote learning or anything at all.
For instance, confronted with a 6th-grader who can't add two fractions with large denominators (because she can't conveniently draw the pie chart), educators say "that's OK, the important thing is that she has deep conceptual understanding." (And how is the pie chart any deeper than the standard algorithm for adding fractions?)
Similarly, confronted with a 7-year-old who can't read because she thinks she should be able to guess everything from context, educators say, "that's OK, the important thing is that she WANTS to read, and she understands a great deal when you read out loud." (That's pretty much what Younger Daughter's first-grade teacher told us at Natural Friends!)
In both reading and math, educators (often, unfortunately, those who train the next generation of teachers) use the issue of "comprehension" to distract attention from the point that their methods don't work; then they promote false dichotomies in an effort to sound "progressive".
In math, the false dichotomy is between "rote learning" and "conceptual understanding"; in reading, the false dichotomy is between "word-calling" and "comprehension".
Now, it might happen that a child could have technical skills without deep comprehension. For instance, she might be able to perform long division without understanding why it works, or she might be able to read a word off a page without understanding its meaning or context ("Mom, what's a carriage return?")
But the opposite doesn't hold. You can't have deep understanding without technical skills. If a kid can't read a word off the page, or add two fractions, that doesn't magically prove that she has deep understanding instead.
Ideally, skills and comprehension should march together hand in hand. Kids should acquire skills and also understand how and why they work. This might be a gradual process; comprehension can deepen over time. Often, comprehension is the result of continued practice of technical skills (one more reason to teach the skills first.)