rate of reaction and RDS
The interpretation of the statement depends on exactly what is meant by &quot;overall rate.&quot;

The rate-determining step corresponds to the largest free energy difference from a transition state to any preceding stable state (reactant or intermediate).
In the example above, the biggest forward barrier is from the reactant to the second transition state, so the second step is rate-determining. However, the barrier, as identified above, is comprised of both the first and second step, so they both figure into the overall rate of the reaction, as determined by the slow step.
EDIT:
Based on comments, I think a clarification is in order. Note that the above conclusion is not true in the general case. You could make the indicated claim for the depicted reaction specifically, but not, for example, in the case below:

The second step here is still rate-determining because the transition state is involved in the largest barrier. However, the biggest barrier is from the intermediate to the second transition state. In this example, I would not say that the overall rate depends on the first step.