How old is your grandson?
I don't have children, so I have no idea what's available in the form of ID for children. For airlines ID purposes, I think a government issued, photo ID is required. Are those available for children? I wouldn't think a birth certificate does any good other than showing that you have in your possession a birth certificate for a child (I'm assuming) that is "x" years of age. That birth certificate doesn't guarantee the airline that the birth certificate is for that child you're traveling with. I know it's a fair assumption. But, without a photo ID, I don't see that there's any way for the airline to check.
About your concerns, if the paperwork you had with you (birth certificate and a letter) would be your bar for acceptable identification; then any good criminal could produce those papers as well. Plus, according to US Dept. of Justice, 49% of child kidnaping is done by parents who would also presumably have the info that you had with you that day. Only 24% are kidnapped by strangers.
www.klaaskids.org is where I found this information.
I commend your concern, but I believe you're putting a heavy onus on the airlines. I don't think it's we want to add criminal investigator to the duties of airline employees.