Same issue recently happened to me HOWEVER i might have a fix. (iphone is currently syncing but songs that were greyed out earlier are now able to play.)
Greyed out songs using iTunes 11.1.3
What i did to fix:
-Under the "summary" tab (when iphone is connected to itunes)
> under "options" check off "Mannually manage music and videos".
-Begin sync
-Under the "on this iphone tab" (where you can see all of your greyed out music)
(at the bottom of this tab you will see your iphones designated file's via colour and the "sync" button to the right of this bar.
>Above the sync button there is a "settings" and "autofill" buttons.)
>Click "settings"
>Uncheck everything
after i unchecked everything all of my songs began to sync.
IMPORTANT:
under this "on this iphone tab" some songs/albums are greyed out still, however when looking on my iphone under music the songs/albums that are greyed out on itunes are on my iphone and do play even though they are greyed out on itunes.
I do not remember EVER turning autofill on. I did however recently update itunes to 11.1.3
Very odd. It might only be a temporary fix, i have 5500+ songs on my iphone will update if i notice this fix does not work.
Ive found about 10 pages since (september alone) on the apple support forms regarding simmilar syncing issues with itunes across multiple iphone models. So if this is exactly the issue you are having you are not alone.
Try it for yourself.
Hope I've helped at least one person.