I've done a fair amount of leather working and my take on the band is this.
Leather has a skin side and a felted side, you can thin the leather down by a process called skiving but any real thickness and durability comes from the thick body of the leather extending into the felted side. It's skin at the end of the day made up of layers.
The classic band uses a modern tanning process and it is uncertain if it is chemically died or uses an iron oxide treatment (vinegaroon) for the black. I'm guessing chemically died.
The material used is skived quite thin and doubled over around the watch lugs. Near the lugs there is an additional leather insert which is stitched in by very small machine stitches to bulk out the shape and ensure there is no visible gap around the bar of the lug.
The straps are then glued, probably with UPVA glue. There is nothing wrong with this, it's durable and flexible. Applied in exactly the right amounts it will see out the life of the strap but one could have possibly hoped for micro stitching. Stitching, however, is debatable because the stitching could cause stiffness in the band.
Stitching only appears to be present on the inside of the band where the pads near the lugs are attached and the belt loop middle.
The edges are then burnished to produce a rounded and smoothed boundary and to hide the join of the felt parts meeting and to make the inserts near the lugs look uniform.
3 layer perception can be summarised as 2 skin sides and 2 felt sides impeccably and strongly glued with no discernible join between the felt side. Simply seeing the skin finish on the inside tells you it is back to backed.
The ONLY bit I can't work out is how sturdy the connection to the ring link on the buckle is and I'm not cracking it open to find out how they did it
I'm pretty happy with it, nice design job