EDIT: Though now that I think about it and, IIRC, Xerox's stuff didn't have overlapping windows either. Apple's Lisa and Mac did. I think Englebart's demo had windows but I'm not sure if they overlapped.
Woz was amazed that it was possible to have overlapping windows on such a resource constrained machine. But if Xerox engineers could do it, he could to dammit! After a Herculean effort he got the overlapping windows to work nicely and they shipped.
It was only later that they found out that Xerox's engineers were blown away by Woz's achievement as they had studied the problem and decided that it wouldn't be possible to do overlapping windows. They never developed that functionality.
Turns out that Jobs had made a mistake in remembering what he had seen and Xerox never did have those overlapping windows :-)
Anyway, this story might be incorrect on some points or a complete fabrication, but I like it.
http://folklore.org/StoryView.py?project=Macintosh&story...
"Smalltalk didn't even have self-repairing windows - you had to click in them to get them to repaint, and programs couldn't draw into partially obscured windows. Bill Atkinson did not know this, so he invented regions as the basis of QuickDraw and the Window Manager so that he could quickly draw in covered windows and repaint portions of windows brought to the front."
Steve Jobs know how important regions were: http://www.folklore.org/StoryView.py?project=Macintosh&s...
In a semi-related matter, does anyone know of the algorithm Bill used to draw RoundRects 'blisteringly fast'? http://www.folklore.org/StoryView.py?project=Macintosh&s...
According to the Apple stories I've read, Wozniak had little to no involvement with the creation of Macintosh. He was in a plane crash in 1981. When he came back to the company in 1983 he was mostly involved with the (increasingly sidelined) Apple II team.
But overlapping windows first came to Apple with the Lisa, anyhow. Some of Bill Atkinson's photos here show them from December 1979 or early 1980. Story says Bill wasn't sure whether they predated Apple's Xerox visit, or not. http://www.folklore.org/StoryView.py?story=Busy_Being_Born.t...
Anyhow, it's a good story. If it has some basis in truth it might be with s/Woz/Atkinson/ (he was their UI/graphics guru programmer) and s/Macintosh/Lisa/. :)
EDIT: The Alto could run SmallTalk as one of its environments, though, and its windows overlapped as of SmallTalk-72 or -76 http://www.esug.org/data/HistoricalDocuments/SmalltalkHistor...