They may not all list it as a hard requirement, but a school like MIT sloan says on their site applicants have an average of 5 years of work experience [1]. You can maybe get accepted with less than 4 but you would need relevant other life experience. (I'm pretty sure HBS listed 4 years when I applied decades ago, but I cannot find a reference)
Ah, that explains it. The business school cohort average age has dropped considerably since you applied. These days it's typical to apply with 2-4 years of real-world experience (acceptance & start add a year to that) and uncommon to apply/be accepted if you're over 30. Keep in mind that average experience statements like the sloan one are heavily skewed by the few old-timers in the programs who have been working for a long time in comparison to the kids who make up the majority of cohorts.
[1] http://mitsloan.mit.edu/career-development-office/employment...