I don't know about your Blackburn Tire that claims to have a carbon steel bead and is foldable. Perhaps it's one single strand of a steel cable they used.. Usually foldable tires are kevlar beads and non-foldable tires are steel beads. Most every one of us on a road bike made this century and a decade or so into the previous century have used foldable tires for years whether we know it or not.

I do seem to remember my fist experience trying to install a foldable tire did leave me thinking they didn't fit. But once I figured it out, they were never an issue again.

Do you know what type rim is on your bike? I'd think it's crochet rims, but if you are putting these on an old Schwinn, you better not if it's a smooth bead rim.