I can adjust what type of vibration/ring/notification etc for specific numbers and text message sources on my SGS3. My Amber alert text messages light up the screen with a notification, but they do not make a sound or vibrate. I don't miss any alerts because I see them when I am up and about and at the same time they don't disturb me at night. Don't most cell phones do something like that? I mean, don't the Amber alerts in NY come from the the same source every time?
If all else fails, can't you put text messaging on silent without putting your alarm on silent? I thought that was a pretty standard thing.