I am Scottish and we always use "just about" to mean "nearly, but not quite".
E.g. "I just about passed my exam" means "I got close to the pass mark, but didn't quite make it."
A straw poll of some of my friends indicates that Australians, New Zealanders, the Irish (both Northern Ireland and the Republic of Ireland) and those from North America (Canada and that USA) also share the same meaning as we Scots. Amongst my English and Welsh friends, I have found that only those from the north of England (Northumberland and Cumbria) share our meaning.
An interesting fact I've noticed that is that everyone says "just about to", to mean "nearly, but not quite", e.g. "I was just about to leave when the telephone rang", meaning "I had not left, but was about to, when the telephone rang".