This has been reproduced with Excel 2013 and SharePoint 2007 SP3.
There is an issue with using Excel Services for SharePoint 2007 to open Excel workbooks that were created with Excel 2013.
If you attempt to open an Excel workbook in the browser that was created with Excel 2013 using Excel Services for SharePoint 2007, you will get an error like this saying that the workbook may be in an unsupported file format, or it may be corrupt”:
UPDATE: The issue is a side-effect of changes/enhancements that were made to the XML for .xlsx files for Excel 2013, which are not present in Excel 2007 or Excel 2010 files.
This issue does not exist for workbooks that were created with Excel 2007 or with Excel 2010.
Excel Services for SharePoint 2013 will open workbooks that were created with Excel 2007, Excel 2010, or Excel 2013.