Pondini,
The Space Gremlin disk usage maps are generated when I responded to your questions. It's not the exact data during my test. So, there will be some small discrepancy.
Finder won't give the free space info. The Availability of Disk as revealed by Disk Utiltiy is the same as that revealed by Space Gremlin app and the same as the free space revealed by About This Mac > Storage. So I know what I am reading.
However, the disk space occupied by Time Machine (and later released to free space) as revealed by Space Gremlin is grouped into "Other" category on About This Mac > Storage.
The "Backups" category as shown at About This Mac > Storage is much smaller than that detected by Space Gremlin.
My guess is:
1. The space occupied, as shown in About This Mac > Storage, is the space occupied by Time Machine Local Backup (Snapshots) and theoretically this space will not grow when the Mac's disk has over 80% occupancy (managed by mtmfs process);
2. The space occupied, as shown by Space Gremlin, is the Time Machine's working area not releasing back as free space until the TM turns OFF. This is the part that I consider a bug, or a programming omission to release unused disk space when not using.
Further information in response to your questions:
The Space Gremlin app is the latest update and it gives correct disk space information on 4 Macs (including the MBA in testing) of different models around me. The disk space information can be reconciled from Finder, Get Info and Disk Utility.
The Sportlight index (as you were doubt about it) has been re-indexed on that MBA. No program.
Conclusion:
Stopping Time Machine Local Backup may not give you back a lot of the free disk space because the working space is not released. To release the Time Machine working space (in my test, about 50 GB), the Time Machine (OS X 10.8.4) ver 1.2 must be turned OFF manually. (Of course, you need to turn TM back to ON to use it.)