You get what you pay for with musical instruments.

That being said, the zero fret was not a defect or cheap knock-off device. Many well-made reputable guitars employ the zero fret. Some people prefer them, saying that if the rest of the notes are fretted then the open note should be too. I have a guitar with a zero fret and it plays fine.

If it wouldn't play in tune, it likely needed a set-up or to have a compensated saddle made. But if it was that cheap an instrument, it likely wasn't worth that bother even. The zero fret does not throw out the spaceing of the rest of the frets. It replaces the nut as the scale length end of the string. That way the nut is just used for spacing purposes laterally across the fingerboard.

I don't know what you did to it to solve the problem, Clean Supper, but it likely improved the set-up. You're lucky in that case.