I've always heard this, too! My sis is a nurse, used to work in LD, she'd tell us stories about teens coming in and having the baby within 20 minutes. Lots of underweight babies, lots of premies. Don't know if those two factors are why the labors go fast for so many of them.
Some people just have quick labors, no matter the age. My first was born 20 minutes after I reached the hospital, and I left for the hospital one hour after feeling labor pains because they'd started out at 3 min. apart. Baby #2's labor was 2 1/2 hours from start to finish. #3 was under two hours. #4, the nine pounder, took five hours and I thought I was going to die! #5 was about three hours. My friends all tell me horror stories about labors that lasted days and days long, and I just zip my lip. I learned the hard way that people who suffered agony don't appreciate those who sneeze and there's the baby!
Editing to add: Over here, mom wears a bracelet, baby wears two and a scan gun similar to those at the grocery checkouts is used to "match" the baby to the parent. It SHOULD be foolproof!