looking at the colour list, there is no black listed, there for, also looking closely at the picture, there is no backstitching.
DD

I know but looking at the chart it is drawn in and the design doesn't look right without it with all the fractional stitiches to leave room for the backstitiching.

Have you already stitched this? I don't see any backstitching. To be honest I think you ought to listen to your gut feeling and backstitch if you want to or don't backstitch it. There are no cross stitch police. Every one of us that does counted cross stitch do different things. If 3 people did this design every last one of them would do something different, Usually, back stitch is 310 DMC or I like 3371DMC. And yes usually it is one strand, Good luck., Peace, Pam