Can you paste the response for us that can't use the model easily?
A real-life example of three events A, B, and C where A and B are correlated, B and C are correlated, but A and C are uncorrelated could be:
A: Ice cream sales B: Temperature C: Energy consumption for air conditioning
Let's break this down:
A and B correlation:
Ice cream sales (A) and temperature (B) are positively correlated. As temperature rises, people tend to buy more ice cream.
B and C correlation:
Temperature (B) and energy consumption for air conditioning (C) are positively correlated. As temperature increases, people use more air conditioning, leading to higher energy consumption.
A and C uncorrelated:
Ice cream sales (A) and energy consumption for air conditioning (C) are not directly correlated. While both increase with temperature, there's no direct causal relationship between them.
So this example isn't good, because when people are eating most ice cream, people are using most air con, both being mainly caused by hot weather. (Unless as you point out we're looking at one individual who wants a solution to feeling hot and doesn't need to do both things together.)