Unfortunately I am the one who made the original board so it is on me. Currently the original svg is breaking Inkscape so once I figure out what that is about I’ll correct the original part.
Works that way in Fritizng too, but the graphics standard calls for drawing units to be in 1/1000in so the size of the viewbox matters (not for rendering reasons but to meet the standard and to make svgs the same format which is useful when making parts.) So I prefer to set it correctly.
I have had a look and see a few errors which I am patching up (and making some changes in the fzp file to not conflict with the original part as the current one does.) When I finish I’ll go through what I did to get there. Can you supply screen shots of how you set up illustrator as you describe? I think that will be easier than what @UniquePete is currently using with Illustrator (which involves importing the svg in to parts editor and then saving the part which parts editor apparently cleans up.) I would like to get a tutorial on how to use Illustrator in Fritzing together. If you know of a way in Illustrator to change the viewbox so drawing units are 1/1000 of an inch (basically the viewbox being 1000x the height and width with dimension in inches) that would be awesome!
Peter