bivariate normal distribution question

#1
My question is based on the defintion available at https://www.statisticshowto.datasciencecentral.com/bivariate-normal-distribution/ which says:

1. What is a Bivariate Normal Distribution?
The “regular” normal distribution has one random variable; A bivariate normal distribution is made up of two independent random variables. The two variables in a bivariate normal are both are normally distributed, and they have a normal distribution when both are added together.

I don't understand why they say two independent variables, when everywhere else it is said that if X and Y follow a bivariate normal distribution they are independent only if the correlation coefficient rho=0. Am I misunderstanding something?
 
#2
The x's are independent of the other x's, and the y's are independent of each other, but the x's and the y's may be correlated with each other.
The x and y numbers are in pairs. They are not normally added together. If you plot the pairs on a graph, they look like an ellipse of random points.