Totally agree with atos72's analysis on the origin of the problem.
And Galileo634's solution works for me to tackle it.
It took me 3 min to install the software ( I happened to be using DiskAid (PC software) + FileApp (Ipad App) ), and delete the whole folder "iPad\Media\iTunes_Control folder",
plus another 30 min for the ipad to download all the purchased app's, which I dare not interupt.
Happily, none of my previous data on the ipad was lost.
But I still can see the broken music file in itunes that caused the problem.
I manually deleted this broken file through itunes, and then dragged all my music over to the ipad from my library. None of them turns grey. Yeah~~
Thanks to both of Galileo634 and atos72.
Hope APPLE can fix silly problems like this.
Below is the credited post by Galileo634.
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Galileo634
I bought an iPhone 5 and could not add music to it. Same problem: grey songs. After hours searching forums and blogs I found this solution. Work for me! Now I manually add songs using iTunes and no problem. Hope it helps.
1. Download and install iExplorer http://www.macroplant.com/iexplorer/
2. Plug in device first, then open iExplorer
3. Delete the iPhone\Media\iTunes_Control folder (you may want to copy this, just in case)
4. Restart the iPhone / iPad
5. Start iTunes. Not restore iPhone from back up, select New iPhone (don't worry, you will not lost apps or data on your iPhone doing this)
6. Add music manually with iTunes