I have the same problem on my iPhone 5S iOS 8.3. When i want to delete a message it appears to be gone. But when i double tap the home button and close the messages app and reopen it. It opens in a new message window, pressing cancel results in an empty inbox. I have tried many things such as restoring from itunes. Completely erasing the iPhone and restoring again via itunes. Deleting the messages attachments makes the messages app as well freeze up. So there is no way to clean up the messages or attachments, other then to completely erase the iPhone and manually install every app and playlist, which i would really like to avoid.
I don't know if it's because of an overfull inbox due to many conversations ( around 2800 messages and 450 attachments), but i'm unable to delete anything now so, Or it is a bug in iOS 8.3? Either way i would like to know a solution different then complete new install.
Does anyone know any hint?
Btw, i tried as well cleaning it up with Ibackupbot but even there the app doesn't respond anymore when i want to delete the messages.