The checkerboard pattern he's referring to is the empty background. no white, No black. It's default.
Two things to do.
1, Check with eye dropper to confirm you have no left over background. This typically comes from a copy and past from another file with a different black color makeup and it comes over not as 100% but like very dark grey black. Not visually noticeable in the other program or in Photoshop at that low of a percentage.
2, Photoshop (file format). Accurip is quirky like that. When printing only one sep, you need to have it in a specific file format. I forget what one it needs to be, but it's either Greyscale, or Multi Channel to make sure it's a spot color and not just a black (process) black) grayscale. (I think Multi) in order for it to read via accurip and psd to print out as a sep.