alt Hacker NewsA BLEVE does not need oxygen to become an explosion. The explosion occurs with the rupture of a tank (that has been heated, increasing the internal pressure and thus increasing the boiling point of the liquid inside, so that it remains liquid). This causes a loss of rapid loss of pressure, which in turn rapidly decreases the boiling point of the liquid, thus causing a sizable part of the liquid to almost immediately boil and cause an expanding "cloud" of gas.
When this occurs, you have an explosion that can propel parts of a steel propane tank up to 1/2 mile (at least).
It doesn't need it but it makes it that much more destructive. Your propane example is such a case - as the hot cloud expands explosively it burns on contact with new oxygen and the heat serves to further perpetuate the process. An overheated tank of propane provides an illustration of the principle on which thermobaric warheads are based.