"I'm sorry for how you feel" is widely accepted as a non-apology in English. Sincere apologies show awareness of how one's actions led to the situation that would require the apology.
It's like how you say "How are you" when you really don't care but it's just how you start a conversation.
The "I'm sorry you feel this way" is quite a recent phenomenon. It started showing up in public apologies by companies and celebrities, purely for PR. It's basically a deflective euphemism for "I'm sorry that you don't like whatever happened" without really admitting culpability, sidestepping all responsibility.
With that said: I don't even know if the author (Kiki) is a native english speaker, since she's part of other language translation groups, so it might be 100% without intent. But that's how a lot of people perceive it today.
"I'm sorry I did that" is an actual apology.
To be clear, I'm agreeing with you. I think that the former version emerged as it's litigation proof. Corporate PR can say that without it being an admission of anything if whatever they fucked up results in a lawsuit.
It has spread to personal communications from corporate ones and it's now so prevalent that it is possible someone might use it and actually mean a real apology. But it's ... tainted.