Yea I just looked at the Burlington building dept site and they just use the MA state code. The rule of thumb is for building code, the most stringent shall always apply. So if the international code says you don’t need a closet, MA code says you don’t need a closet, but for some reason Burlington had a requirement for bedrooms to have a closet your realtor would be correct.

Side note, could you DM me any info on the listing? Have some friends house hunting in that area. If not I understand. I also have a great long time friend who is a realtor in the area (one of Bostons 40 under 40) who could help you if you aren’t happy with who you’re working with. Best of luck!