Really? We don't need to go far to prove you wrong. Let's use your home state as an example. The Texas Department of Vital Statistics says:
Short form birth certificates can usually be produced in 30 minutes to 2 hours. If you need a long form birth certificate, it may take several days to process.
http://www.dshs.state.tx.us/vs/reqproc/certified_copy.shtm
They call both the long and short form documents "birth certificates."
Tell ya what, sparky. You take your short form bc down to the local Texas DOT and try to get a driver's license with it. If you're successful in obtaining one, I'll concede in public that you were right, and that I was flat out lied to by my local DOT officers.