Correlated one time pads require to use the same key. If the one time pads use different keys, they do not constitute a counterexample.

Thanks for comment. $\leftarrow$ means randomly choose an element from the corresponding distribution. || stands for concatenation. And I have considered correlated one time pad as counterexample. However one time pads are not CPA secure since they are deterministic. With the property of CPA secure, it might be possible to achieve security by concatenation.