I'm with a little question.
What happens to the edited file after saving its copy using the “Save for Web…” command? Why the original, unmodified file turns into “changed” (with * symbol after its name)?
P. S. The same behaviour is in the Illustrator.
It's because the original file did get changed, because the Save for Web settings were changed. Photoshop saves most Save for Web settings so that the next time you use Save for Web, you don't have to set all the options from scratch.
I tested this by opening a file and using Save for Web without changing any settings, and that time the original document did not ask me to save before closing.
It seems to be that it saves all but the Image Size for export.
I was misled by this because changing this parameter took no effect when I reopened the document and went to "Save for Web..." menu again.