That is not true.
The miners do not know who is sending the bitcoins, or where they are going.
As long as you have access to an output from the transaction, you can spend that output and include a fee large enough to pay for both transactions. In that case any miner (or pool) that has implemented CPFP will consider the increased fees when choosing which transactions to include in their block.
When you say "access to an output from transaction", what does it mean.
If you don't mind could you please explain.
Thanks