There are a number of possible explanations, of which I will list just a few:
1. The cognitive testing may be a low estimate, perhaps a function of his test behavior/engagement on that day. I believe this was one of your concerns; it does appear less likely, where you have another cognitive assessment that is very similar.
2. The type of academic skill and knowledge development expected from a late K/early 1st student is heavily weighted toward rote skills (basic decoding, sight words, addition facts). A child who can pass basic skills and begin demonstrating any level of higher-level reasoning or application will rapidly escalate into the upper reaches of standard scores. This may be an artifact of the shape of the NT growth curve at this young age. As an example, the skills exhibited by one of our kiddos at age 4 or 5 would have resulted in scores in the same range as your DS's. (We've never had the children formally tested, but I've tested hundreds of other people's children, and have a pretty good idea of where they would fall.) This child is bright and clearly GT, but certainly not PG.
3. Achievement scores are much more sensitive to difference in instruction and educationally-supportive environment than cognitive scores are (by design, in the latter case), though of course, all tests are, on some level, tests of achievement. They are also intentionally "school-y", and thus a measure of performance on (usually) familiar task-types. A child who does well with routine may perform better. Cognitive assessments are supposed to be tests of one's approach to novel tasks, so they should not favor those from environments with more exposure to academic-type activities. (In reality, of course, they still do, though not as much as overtly academic achievement tests do.)
