Yes, the way it works in IBJJF rules is that blue belts can give stripes to white belts, up to 4 stripes. They are not allowed to promote to blue belt.
Purple belts can promote up to blue belt 4 stripes.
Brown belts can promote up to purple belt 4 stripes.
Black belt 1st degree can promote up to brown belt 4 stripes.
Black belt 2nd degree can promote up to black belt 1st degree.
And so on.
Not all martial arts do it this way. I don't have any insight into how or when this started in BJJ, but if you think about it, it's the quickest way to spread the art and retain a high level of quality. Otherwise you'd need to quickly promote lots of people to black belt, even though they're not ready for it. Then you would need to send out those limited numbers of black belts all over the world to start up schools. And they would be promoting people much more quickly, weakening the style. Whereas, what BJJ did was to attract students from all over the world to come to Brazil and then go back and teach it wherever they're from. When a blue belt teaches a white belt, they really work the white belts hard and ensure the white belts know everything the blue belts have been taught. It worked out rather well for spreading the art and maintaining quality, in my opinion.
As for blue belt "instructors" giving stripes to white belts, this used to be more common when BJJ was relatively new to the world. In the early and mid-90's when the UFC had just shown BJJ and grappling practitioners dominating everyone else, there was a rush to learn BJJ. But there weren't any black belts around, usually. The best you typically could find was a blue belt. So you had to learn from a blue belt. And they awarded stripes to white belts.
Notice I put double-quotes around "instructors", because they weren't really given the title of "professor". That comes at black belt. But exceptions were made when there weren't any black belts around in the local area. So blue belts could call themselves instructors or coaches.
Nowadays, it's much more common to find black belts in pretty much every major city. So it's rare to see blue belts who have the title, "instructor". The word, "coach", is more acceptable. They can and do still train people and award stripes, but when it happens, they are almost always affiliated with a black belt instructor who has given his/her blessing to the blue belt. It's not taboo. The black belt might even come to the school to oversee the training and be there in order to promote people to blue belt and above.
I remember living in Houston in the mid-90's. They just had a small number of purple belts teaching back then, for the entire city of 4 million people. It took maybe 4 years after that before I started seeing the first black belts opening up schools there. Whenever a black belt moved to town, people took notice. These days, people are spoiled with how many black belts they have available in every major city.
Hope that helps.