@layman,
OK I see what you are doing. You have a
philosophical misunderstanding of what the theory says. You are claiming (incorrectly) that under SR both clocks should have slowed down.
You have backed up your philosophical misunderstanding with quotes from Fenyman and Smoot, which you also misunderstood. I think you started with the first philosophical misunderstanding, and then distorted Feynman and Smoot to match.
But let's look at what the paper by Hafele and Keating says.
1). They go through mathematical detail on how they made their predictions. The paper literally goes step by step.
2) The predictions are that the Eastward plane should lose 40ns +/- 23.
The Westward plane should gain 273ns +/- 21.
3) The measurements were that the Eastward plane lost −59ns ±10
The Westward plane gained 271ns +/- 7
This is a successful experiment. The experimental results matched the theoretical predictions quite well.
The bullshit you are reading on conspiracy sites are apparently claiming that Hafele and Keating lied.