This doesn't look right. I couldn't get the BB cup to spin even one revolution without resistance. I'm worried about cross threading. The seller told me a BB didn't do this. I agree; it doesn't look like it's had one on it in some time, and I wonder if this frame was hung on a hook or something through the BB opening and it caused the damage (it extends the entire width). I wonder if I should keep it and get my LBS to rethread or install a threadless BB.

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one possibility might be that the first thread was damaged by an impact

it that be the case a thread file or an

old cup cut into a chaser would be adequate to clear things

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First get in there with a wire brush

The only thing I see is the weld seam from the production of the (very cheap) bottom bracket shell. Running taps through the bb should clean things up satisfactorily.

I suspect that what you're thinking is thread damage extending all the way across the threads is actually the weld seam on the bottom bracket shell. That type of shell is bulge-formed from sheet metal to create the sockets for the tubes, then wrapped into a cylinder and welded closed before cutting the threads. It's likely that all you need to do is chase the threads, as others have suggested. Grease on the threads will also help. If you still have problems, seek a bike shop that has professional-grade, piloted bottom bracket taps to get the job done right.

Neighbor had a tapping tool, all is well.