It's either what newey said or that wire is the type that has two layers covering it: black cotton and a metal braid. Very common in vintage-ish Les Pauls.
The technique is simple, push back the metal braid, push back the black cotton (revealing the the wire transporting the signal) solder it in place and then just keep the metal braid away from anything transporting signal.
Ok, so it is a push back type, very nice, and easy to work with. When i first worked with push back stuff for my tweed amp I was trying to cut the darn stuff and super glue the ends until I realized how simple it was to get a nice square sharp cut and push the stuff back.
I assume that soldering the outside braid to the pots is pretty straight forward. Tin the pot lay it on apply heat and add solder.