It's not his secretary, she's his chief of human resources. It's essentially her entire job to prevent these kinds of relationships. there are likely legal ramifications and the company is gonna take a hit regardless.
But that's not the issue so much as the fact that the CEO then turns to social media to give the most vague apology ever and then starts attacking the general public because a "private moment became public without my consent". He literally brought his side piece to a public event with cameras broadcasting across the nation and blames everyone else that he got caught.
It's honestly pretty scandalous on it's own, but his reaction is what makes it so delicious.
CEO cheats with his human resources chief and blames the general public for it. That HR chief has likely fired people for similar relationships within the company. Says the public is at fault for violating his privacy at a public event. Everyone is pissed for some reason or another.
Could have just cheated with anyone else and it would have been a personal matter, but the situation and his reaction have been pretty bad.