Sounds like you can bring a baby in the restaurant ... just not the stroller. Its an understandable rule. Strollers are bulky, and get in the way of other patrons and the waitstaff.
Who brings a stroller into a restuarant, anyway ... nice or otherwise? We always brought either the carrier (when the kid is too small to sit-up) or just the baby. Never had a problem.
Then again, we live in Houston.