What are you doing with the string? Putting it on the model?
No need. If you do measuring correctly, you don't have to worry about pinpoint accuracy, because it is a self-correcting method (as long as you keep measuring, and try to get it close each time)
Don't measure on the diagonals! Only measure horizontal and vertical elements, because if you add the extra dimension of angle to the measurement process, it's one more variable you have to manage.
Always make your measurement at arms length (for consistency) with the tip of a skinny stick (like a wooden skewer, or a pencil if you have nothing else).
If you have to measure on your drawing (and you probably will), use a piece of paper with tick marks. Again, horizontals and verticals.
If you're consistent about this approach, it will be like throwing a loose grid of squares around the model, which will "tighten up" slowly as you take more measurements. You'll end up with a very accurate drawing in very little comparative time.
It takes practice, but not too bad before you can do it accurately. Trust me, I know all about the pains of worrying about being "not accurate enough" with measurements. Trust the self-correcting nature of the beast, and it will become much easier.
He's using the string in place of a skinny stick. It's like the skinniest stick you can find, and you can always be sure it's straight (I often use knitting needles, which are prone to bending). I like the stick myself, but I know others who prefer the string.