Ok after a lot of research, it appears that Pure Sine Wave Battery back-up units only output the pure sine wave when not plugged-in. The problem here is you need big a$$ batteries to power your rig for a reasonable amount of time.
If plugged in, the units can still output a pure sine wave but mixed with "filtered wall AC."
Can any of you "Battery-people" share your rigs so we can see how you're getting your pure sine wave AC?