As can be seen from the debug image when I call SystemUpdate(false) of a SPItem, that SPItem's File object's ModifiedBy attribute changes to "SHAREPOINT\system". Sorry, it's a bit weird way to present it :). 'destinationFile' is an SPFile object. And since the object is not the same as the one in the Database after SystemUpdate call, it doesn't change on the debugger.
But why? It does as promised and it doesn't change the item's ModifiedBy etc.. But the SPFile object under it does change.
Anyway, how can I make sure both SPItem.ModifiedBy and SPFile.ModifiedBy don't change after I make some changes on SPItem.Properties?