Absolutely not true! If currency in excess of $10,000 (in or out) was involved in the transaction, you must file a CTR whether or not a SAR is filed. The one is not connected to the other.
Now, if they were going to conduct a transaction that would have triggered a CTR and changed it to less than $10,000.01 when they found out about the required information, you would file the SAR and no CTR. In that case, however, you are not filing a CTR because the transaction was less than $10,000.01. It has nothing to do with the SAR.