All I can say is I've never had a problem boarding an RCI vessel - or those of any other line. The cruise line has an obligation to comply with federal law. It is not a cruise line rule about the birth certificates. The cruise line can get in serious trouble if they allow someone to board with documentation that might later be found insufficient by Immigration authorities when you exit the ship. Obviously RCI didn't think your birth certificate was the original but instead just a copy.
I happen to like RCI a lot and will cruise with them countless more times in the future. As for the BBB - many like to hold the BBB up as a shining example of righteousness. The fact is they probably list most large corporations as having questionable advertising.