Do I owe tax in a state where I don't live or work if my employer says my wages weren't reported there? Even if the two states appear on my w2?

I have always lived and worked remotely for my company, and I never travel to work there or have the option to work there. There are two states on my W-2, but I don't think I have any tax liability to the nonresident state. I asked them to correct my W-2, but they said they couldn't, and then added that my wages were reported to the IRS and my resident state only, what does that mean? That I don't need to file a nonresident return? 

I haven't had anything withheld from either state so I am not worried about that. It will just cost me an extra $300 for the nonresident state, even with a credit on my resident state return.