Reading the title of your thread, my initial thought was that high achievement does not require giftedness. However, in the context and at the level you describe, I'd be inclined to say that it is a reasonable indicator of giftedness.
Where I am not sure that achievement means giftedness would be somewhere like this:
- my kid reads above grade level, therefore he is gifted; or
- my 5th grader is testing in the 96th percentile on a grade level math test, so he must be gifted; or
- my child is a straight A student, therefore he is gifted, etc.
When you start getting to the point where a person is well above the 99th percentile across the board on achievement tests or is such a stand out student that he gets massive attention beyond his school, the likelihood is good that he is gifted.
