Falling interest rate callable/non-callable

[prodigal]

When interest rates are falling, callable bonds underperform non-callable bonds due to negative convexity. If I cannot recall the convexity info in the exam, can I rationalize by saying that “when interest rates fall, the issuer will call the bonds since they can borrow money elsewhere at a lower rate. Thus if you are long the call bond, you dont capture the cash flows - hence a non-callable bond will outperform”?
Did I get this right?

 

[Galli]

More like the option on the bond is worth more to the holder (the company) which reduces the market value of the callable-bond.