A while ago, an image of the tape recorder used on the Galileo probe was posted on the /r/electronics subreddit, and there was some discussion about the construction technique used. Here is one of the images in question:
To me it seemed like something that would be used in a prototype, and not in a flight ready system. So I googled around a bit more. It turns out the tape recorder used in Galileo was fraught with problems, and almost killed the mission. It was provided under contract by Odetics, a company based out of Anaheim, California.
My first interesting find was the image the follows, which clearly shows the same style of construction:
A bit more searching led me to a patent filed in 1980 by Odetics:
CONTINUOUS THRU-WIRE WELDING MACHINE
CONTINUOUS THRU-WIRE WELDING MACHINE ...As is known in the art, the continuous insulated wire is snaked to individual terminal locations without the need of removing the insulation prior to assembling...
I guess that answers that.