Not to defend their cheating, but when you saying "I cheated" ends your career and the career of everyone involved with you, it's easy to see why they may dig in. It's not some game for them, this is their livelihood.
There's probably more recent ones too, this was posted here recently so was on my mind.
No? By denying it there's still a chance you'll get out of it, however tiny that chance is. That chance becomes zero when you admit it. A "shred of integrity" won't pay your trainers mortgage.