I think the BBC’s use of the verb phrase “jumped out of windows” in this sentence that you presented is perfectly grammatical and idiomatic: “When the house caught fire, people jumped out of windows in a desperate attempt to save their lives.” “To jump out of something” is to leap from something, often as an act of panic or desperation. In that sentence, we get the sense that when the house was on fire, people clambered up to the window ledges, stood there momentarily, then jumped.
That same sense of urgency and peril is evoked by the use of “to jump out of” in this lead sentence of a news story: “Two people were arrested after they jumped out of an SUV that crashed while trying to avoid a traffic stop.” In milder form, that sense of making haste to avoid an undesirable or unpleasant outcome is evident in the phrase “jump out of” in this sentence: “That day of my job interview, I jumped out of bed when the alarm clock rang.” And, of course, the sense of going from a bad situation to an even worse one is captured by the verb phrase “jump out of” in the idiomatic expression “to jump out of the frying pan into the fire.” It should then be clear by now that the BBC story had not misapplied the preposition “out of” in its use of the phrase “jumped out of windows.”
At any rate, let’s consider your suggestion that in that sentence, “out of” be replaced by “through”: “When the house caught fire, people jumped through windows in a desperate attempt to save their lives.” Does that sentence still convey the same sense intended by the original? I don’t think so.
Grammatically and semantically, though, there’d be nothing wrong with that sentence if, in fact, that was what the people in that burning house actually did in their effort to save themselves. But I would say that under such circumstances, the act of “jumping through windows” is highly unlikely. It evokes an irrational and illogical scenario—that of people making a dash from somewhere inside the house for a quick, unthinking jump right through the window without even considering the risk and consequences of doing so. Even for people under such terrible duress, that kind of behavior is highly improbable. People will jump through a hoop for the fun and thrill of doing it, and they would jump through a road barrier if they think it’s not too high to cause a bad fall, but they won’t jump through the window of a burning house without first assuring themselves that they won’t be jumping to their certain death, which, of course, would be jumping out of the frying pan into the fire, so to speak.
