You're right, from usually denotes an origin, meaning you transform the material FROM A to B, or that B originates with A.
Through is a metaphorical use, as it means inside, across, and out the other side; so here it indicates the means, rather than the matter itself. There is quite a lot of flexibility and modularity with English prepositions, though, and you'll see lots of examples that seem to belong to the other category, but which are frequent enough to sound 'dominant.'
Maybe you can answer something I've always wondered. I learnt Portuguese in Setubal, south of Lisbon, but had a Brazilian girlfriend (!!!!!!!!!!!!) for a year or so -- after -- falling in love with Joao Gilberto, Maria Bethania, and Jobim and the gang.
How I listened to Brazilian music has always been very private -- I just gradually interpreted the meanings myself, as I slowly became more aware of the words. In the unofficial anthem, Aquarelas do Brasil, I always pictured "inzoneiro" as meaning something like a sorceror or enchanter, and I always thought of "ginga" as a sort of a dance. But I can't find a reliable dictionary entry on these.
Meu Brasil brasileiro
Meu mulato inzoneiro
Vou cantar-te nos meus versos
Ô Brasil, samba que dá
Bamboleio, que faz gingá
Ô Brasil do meu amor
Terra de Nosso Senhor
Prá mim... prá mim...