I offered a definition of "reward" in the comments section of a previous post and wanted to bring it front and center--for comments. Here it is again: a reward is something given or received in response to or recompense for some action.
Notice that this is very close to the standard dictionary definitions for the term. The Free Dictionary, for instance, defines the term as something given or received in recompense for worthy behavior or in retribution for evil acts.
Central to the concept of reward is compensation, or justice. The concept is wide enough to include responses to good or bad actions. And it leaves open what is good or bad (as it should given that it's a broad definition).
Some examples: paying a salary to an adult for providing work agreed to, paying a child an allowance for doing the same, buying a friend a beer in honor of a good story told, buying a toy for a child in exchange for demonstrating some skill, celebrating an achievement with anyone for something great, and so on.
The concept of reward, broadly defined, also leaves open who or what (in the case of reality) is providing something in response to some action. In any case, given the above definition, to be anti-reward, literally means to be against giving or receiving something in response to or recompense for some action.
While agreeing that a child's primary feedback should come from reality, I will be making an argument (at some point) that there is nothing wrong with rewards--so defined--and that there is nothing wrong with incentives either.
As a preview, here's a brief point: Some grown-ups never have the experience of getting paid for something they love to do. When they do get paid to do that thing which they love they do not become second-handed or focus on the payback. They love it all the more, because what gives them happiness internally improves their situation externally (in this case more money to spend). Letting kids experience this seems like a good--and not a bad--thing. Especially within a proper context.