If it's an apology, why do I think he's full of it?

We had a guy write us about apologizes. Here's what he asked and our response.

"I'm a 15 year old boy, and I read The Guide and really found it useful, so thank you for that. After reading the section on fake apologies, I wanted to ask your opinion on using, "I'm sorry if you feel that way" as an apology....

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"On the one hand, it acknowledges the persons feelings, but on the other, it assumes no responsibility for them. I think when you get a sorry like this, you are entirely within your rights to say something like, "Ok, but saying that can come across like you don't think you did anything wrong. Am I right?" 

Here's our advise:
When you get a sorry like this, you are entirely within your rights to say something like, "Ok, but saying that can come across like you don't think you did anything wrong. Am I right?" That won't solve the problem--meaning the person will give a more sincere apology but at least they don't get to get away with giving a crappy apology. Because the thing about apologies is precisely what you said--a true apology takes responsibility. 

What would you have said?