Reinforcement and punishment are not what I would call the units of insight of behaviorism. Behaviorism stands for the proposition that behavior modification does not require a self-reflexive cognitive component.

But making those kinds of changes requires a rigorous analysis of the function / purpose of the behavior (escape, attention, etc). The labels "reinforcement" and "punishment" are intend to focus on the key point of behaviorism: Frequency of behavior - without reference to beliefs or feelings - is the only acceptable data.

Once that point is made, I accept that defining "reinforcement" (as stimuli that increase or sustain the frequency of behavior) does not stand on its own as analytically useful in changing behaviors.

Also, stimuli is not the technical word, but I'm not an expert on Applied Behavioral Analysis.

Consider the story I heard during a lecture on ABA:

A patient at an in-patient mental health institution was engaging in "garbage talk" that the care providers wanted to extinguish (don't ask me why this was a priority). They determine that the function of the behavior was attention, and implemented a protocol (i.e. told the staff to stop interacting with the patient when she engaged in garbage talk). This intervention reduced the occurrence of garbage talk around all but one attendant.

When this discrepancy was noticed, the attendant was observed, and "ignoring" was implemented by that attendant as follows:

P: Garbage talk
A: I want to warn you that I'll start ignoring you if you keep doing that.
P: Garbage talk.
A: Ok, I'm going to start ignoring you.
P: Garbage talk.
A: I'm currently ignoring you.

Needless to say, that didn't work at reducing garbage talk. Perhaps if the attendant had worried less about making sure that the patient "understood" the intervention and focused solely on frequency of the behavior, then the attendant wouldn't have made this mistake.