No, you did not read that wrong. Of the southern African states, Botswana was pretty much the only nation to have not suffered a coup, a civil war, major ethnic or racial unrest, in the same way that much of the rest of that section of the continent did.
The path of Botswana is a rather interesting one. It gained its independence from the United Kingdom in September 1966. It started off as one of the poorest countries in Africa, however these days has proven itself to be an "enduring multiparty democracy with a record of sound economic management, that has used its diamond riches for national advancement and maintained an administration free of corruption" (Martin Meredith, The Fate of Africa: A History of the Continent Since Independence. pp. 786) in recent years.
The main reason that Botswana has managed to avoid the fate of the likes of Angola, Mozambique, Namibia, is largely in its process of decolonization. Relatively speaking, Botswana, as noted above, was granted independence relatively lately, in 1966. This means that in many ways many of the missteps that occurred in the British decolonization of the rest of the continent did not occur here. Its first president, Seretse Khama, was a nationally renowned figure, and a chief of a major tribe of the Tswana ethnic group. His particular tribe, Bamangwato, had broad support throughout the country, and Khama himself was a forward-thinking individual committed towards democratic governance. The Khama government focused its attention on internal matters, diverting much of its funding into social aid such as improvements to the country's healthcare system, its education system, and its transportation infrastructure.
All of these investments slowly but surely started to improve , and while it would take decades, Botswana was generally on a course of improvement and it generally was able to avoid the rampant corruption that also plagued other governments in southern Africa. That corruption and incompetence was often a driving factor in various conflicts and civil wars in the other countries you noted.
As such, there was no colonial war going on in Botswana, much as there was in Angola or Mozambique, nor popular uprisings against the government as in Angola after the War of Independence and the Portuguese withdrawal. Likewise, ethnic tension was largely
Ethnically speaking, Botswana has largely managed to also avoid a lot of those issues. Unlike in Zimbabwe (then Rhodesia) while there was a notable white minority, they did not try to contest majority rule, and indeed the white population was never turned on by the government, unlike, again, in Zimbabwe. Indeed, some White Rhodesians expelled by the land reforms under Mugabe moved to Botswana to establish themselves there. Further, there has been a general sense of inclusiveness within Botswana's political parties, and unlike the political parties of other nations, almost all parties in Botswana are ideological, and not ethnic or regional in nature.
Further, Botswana was able to avoid conflict through the nationalization of certain key aspects of its economy quite early on. The diamond and mineral trade in Botswana is wholly nationalized, as is the cattle industry.
Botswana's strong democratic institutions have also played a role. While the Botswana Democratic Party, founded by Khama, has won every Presidential election held in the country, the nation has been politically very accepting and tolerant of political opposition in government, and the country is one of only three nations (with Senegal and Gambia) to have held consistently been able to sustain (reasonably) free and fair elections with a multiparty opposition on the ballot between 1960 and 1989, the years where these kind of conflicts were most rampant.
This is not to say of course that Botswana has not had its own share of issues, or that it is some sort of perfect nation in the middle of a restless continent, but the factors noted above, as well as others helped to essentially create a sense of stability and prosperity and a social stake in the health of the nation by many people that has managed to ward off the specter of civil war, revolution, or regional conflict.