Does that mean I could buy one copy of an app and install it on every Mac in my business?
No, the license you agree to when you enter the Mac App Store says that app downloads are for Macs that you personally own, and that's a license for personal use. Apps that are intended for professional use are licensed for you or for a single computer used by several people. While there's no technical impediment to you installing them on multiple Macs at work, you'll be violating the license agreement. It's the same scenario as if you buy a single-user copy of iWork and install it on ten Macs at work—you can do it, but you're violating the license agreement, making the act ethically questionable.
We know about the volume licensing that Apple offers, but it seems as though it's only for education and not for the enterprise. Surely creating a new Apple ID for every Mac isn't the best way to do this, right?