Age in itself is not a criteria for rejection even at H/S. However, if you are 31-32, the onus is on you to explain what you bring to the table. As we all know that a large number of exceptionally qualified 25-26 year old apply to top schools. So if someone is say 31, they needs to articulate what they have done for those extra 5-6 years. There are 2 generic scenarios:
1. A guy at 31 figured out his career a little late and is hence essentially at about the same level of career progression now as a 25-26 year old bright kid. Therefore he loses out to them.
or
2. A guy at 31 has had an exceptional career progression and was perhaps an ideal candidate for top MBA when he was 25-26. However, his career progression now has taken him to a point in his career where a full time MBA becomes irrelevant.
That's why we see successful 31-32 year old students at top schools generally have a phd, a medical degree,have spent time in the military or have unconventional career paths (NGO, self-employed). These people are successful because they have perfectly valid reasons for applying late in their careers. On the other hand, there are enough 25-26 year old conventional applicants - investment bankers, consultants and IT professionals - who are at the ideal time to apply. Therefore, a 31-32 year old in this pool will lose out because of (1) or (2)
Essentially, it comes down to your accomplishment/career progression since you completed undergrad (Its important to note that HBS talks about years since graduation and not about age which is not necessarily the same thing). Most top business schools feel that 3-5 years out of undergrad is sufficient for most people to be ready for an MBA degree. However, if you apply later in your career, they expect you to have a compelling reason. It seems fair to me.