Thanks, a.l.e. Here is the Scribus file and the Scribus and Indesign pdfs. I can't attach the Indesign file.
Both pdfs are opened correctly by 2 browsers (Firefox and Safari) and by 2 versions of Acrobat. Neither is opened correctly by Preview, which makes the first page a right page and therefore muddles up all subsequent pages too, giving right pages the left-hand layout and left pages the right-hand layout. It was true but misleading for me to say in my first post that Preview opened the Indesign pdf correctly, because in the indesign-generated pdf I was using then the spreads were saved not as facing pages but as single pages, twice as wide as usual. Presumably that was why they opened correctly in Preview - it wasn't given the chance to misplace the first page. Sorry about the confusion.
It seems that, as you suggested, Scribus works fine, and that the problem is with Preview.
Thanks to you and Nermander for your time.