I've always suspected as much but never actually checked it out until now.

It appears that when importing a background, Poser will scale this image to the size of your current composition window (not your render size). It will then use this resampled image for both your working display in the composition window, as well as the render.

For example, create a grid 800x800 and import it as a background image while your composition window is at 800x800 and it renders OK. -- Import this same image while your composition window is at 300x300 and it gets all fubar in the render.

Same background image, different results depending on the current size of your working composition window.

It would therefore appear that you cannot get a background image to render at any resolution higher than that of your working window, regardless of the original background image size or final render size.