Kelsey Grammer -- We Put Baby in Car Seat BEFORE We Left the Airport

Kelsey Grammer claims he and his wife DID secure their baby in a car seat before they left LAX yesterday.

Grammer's rep tells TMZ ... at some point, before the family left the airport grounds, Kelsey loaded up a car seat and strapped baby Faith inside before they hit L.A. city streets.

Since the footage we posted earlier appears to show Kayte and the baby inside the vehicle WITHOUT a car seat, the rep may be insinuating that the car circled around the airport and picked up Kelsey, who eventually retrieved a car seat. It does appear ... after Kayte and the baby drove off, Kelsey went down to baggage claim and picked up the luggage that was checked.

As we previously reported, it's against CA car seat law to have a 4-month-old child inside of a moving vehicle without a car seat ... so even if the car JUST circled the airport, they still broke the law.

So, we gotta ask ...