My experience with extra tests required by a CAA for the issuance of a Class 1 has always been that I've had to pay for the tests as required although I've not had to pay the CAA for any extra work expended by them in approving the results.
When it comes to stress ECGs, my experience has aways been that a CAA or an AME might administer such a test. However, since a heart attack is quite a possibility for an older person when doing a stress ECG, I don't mind at all if the test is administered with a cardiologist present. This may be from where your CAA is coming.
This is just conjecture based on my personal experiences as a Class 1 holding pilot. I hope it helps.