Hi,
I posted for two reasons.
1) the Original post is tagged as a Messages Issue (It might be tagged with all the options but you are no longer shown the tagging info) and I thought I might be able to solve it.
2) I don't have the issue.
The App can play the System Sounds as these appear in the list.
It can also see the sounds that might be in ~/Library/Sounds in your Home folder.
These might not be heard if the System Alert settings has the volume turned to low (it is independent or the master volume).
It may not play if you have lost permission to Read the individual File or in some cases the Folder it is contained in. This is unlikely for System Sounds however it might be an issue for the ~/Library/Sounds folder.
In a Finder Window use the Go Menu > Go to Folder option.
Copy the Bold path above and paste it in the Dialogue box.
Next in the Finder window use the View Menu and then > Show Path bar.
Highlight an file if there are any in here.
Right Click the item and chose Get Info.
In the Info Panel scroll to the bottom
Your Shortname should appear.
Highlight this and Unlock th Padlock.
Then use th Cogwheel type icon under the list
This should show you the option to "Make yourshortname (Me) the Owner" but it should be greyed out if you already are the owner.
If you do right click on the icon for the containing Folder (in this case, Sounds) and check you own that.
The default of the System Sounds is that they can be Read by anyone.

8:05 p.m. Sunday; October 18, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad