Does iTunes merely lie or does it plan to wreak havoc?

Question

iTunes 11.1.3 running under OSX 10.8.5 may not update apps installed on my 64GB iPad-3 (with iOS 7) merely by invoking Sync [a mis-feature that appeared after iOS7 was installed].
In iTunes, if I click on the Update button for an app, that button changes to say Will Update, but the status bar below will also show installed storage for apps shrinking to a trivial value --- the "Free" amount goes from 9gb to 50+gb and app count drops from 1000+ to below 30.  This signal of a drastic change also appears if I try to install a newly purchased app.  In each case, I have invoked Revert rather than lose my crafted installation of apps.
My feedback via iTunes (7 days ago) about this has elicited no response from Apple.  It is not clear whether I am seeing a benign bug involving a drastically incorrect display or correct display about a gross bug involving a drastic failure to maintain existing structure.

Answer 1

Q: iPad sync'd with Mac/iTunes Media Library before?
A: yes, regularly without error from Nov-2012 through Oct-2013
After a long discussion with Apple Tech Support for iOS, being on-hold while tech did some research, having phone connection broken at Apple's end, waiting 3+ hours for tech to reconnect via my call-back number, finding no voice message from Apple after I returned from some errands, re-phoning AppleCare only to learn they closed early on Thanksgiving-Eve, I decided to proceed with two standard procedures.  (Note that Restore Backup is a much simpler procedure than Restore iPad --- those commands appear in different blocks of the Summary tab within iTunes.)
0)  iPad connected via USB to Mac, backup the iPad via iTunes
1)  Restore Backup: no change in behavior
2)  Restore iPad: accept "Restore … to factory settings", then choose Restore from Backup.
Note: the backup does have details about the several pages, their various folders, and the apps in those folders.  The "Restore from Backup" phase had multiple occasions where the Apple icon appeared together with a progress bar indicating the device was rebooting ---- I suspect restoration of each page was followed by reboot.  After the page structures were restored, then apps were downloaded from the Mac ---- about 10 hours with several interruptions for rebooting.  Because this restoration was incomplete (several folders had unusual icon and apps within were labeled "Loading…"), I needed to do 2 or 3 subsequent Snyc's to clean up.
     RESULT: no change in behavior.
a) updates not installed
b) selecting an update or new app to be installed causes the dramatic signal of lots of used space becoming "FREE"
Eventually, I invoked Apply after seeing visual signal about possible havoc --- the result was installation of the update (sometimes requiring a followup Sync to complete a load).  On several occasions, installation of a new app triggered a reboot of the iPad.
During a Friday call with Apple Tech Suport, the tech urged me to restore the iPad as a new device, reinstall my stuff, and see whether the bug reappered.  His chief rationale was the idea that my backup had a software bug.  Since the backup file should have no software, I will escalate my next query to upper-level support when I phone on Saturday.  In any event, creating by-hand a human-readable record of my iPad's organization would take several days to create and several additional days to then recreate that structure.  If I evaluate that in terms of billable hours, it would be cheaper for me to buy a new iPad.