My kid didn't get an interview for Reception, either, but then again, very few do. I do have one colleague whose son got an interview and got in, and they are not in any of the priority categories. I have met her son who is about 6 months older than mine, and he is extremely well-spoken, articulate, and mature for his age (he started this fall at CIS and is now 5).
Other families I know who have gotten in have seriously tried to work their connections to any of the trustees, staff, etc. One family got to know many of the trustees by becoming a board member of a charitable organization many of them serve on. Another father wrote letters explaining his unique position within the journalism community and what he could offer to the school (he was the head of the Asia bureau for one of the major int'l newspapers at the time). The school definitely likes having a who's who among its parent community, so for regular folks, the key is to make yourself stand out in a good way.
I think it is virtually impossible to get in considering the over 900 applicants they get for the Reception spaces -- the odds are not in our favor. At the higher grades, there is very little movement, so it doesn't seem to get much easier as the kids are older. Maybe others who were successful have some additional advice.