I think she means that she used multiple circular needles to accommodate all the stitches around the outside of the blanket. If you have used double pointed needles, like to do the top of a hat or a sock, it would be the same idea. With double points you have 3 or 4 holding the stitches and use an empty needle to knit onto. I have never done this with something big like a blanket. Usually with a circular needle you don't really empty the needle ever, you just keep going around and around, but maybe when you use them this way you would empty a circular needle just like you do with the double points. It sounds like she had one circular holding the stitches of each of the four sides and knitted with a fifth circular.
I'm not sure how she did the corners though. I don't have access to the pattern, but if you didn't do something to allow the corners to increase they wouldn't lie flat when you finished. It sounds like the pattern called for doing the sides each separately, as directed and then sew the corners together. I'm not sure how the lady who changed the pattern handled that aspect of it. Maybe it is possible to do the shaping given in the pattern, but just carry it on around and avoid the seam.
Maybe if you contacted the blogger she would we willing to help you figure it out. Good luck.