The article does make some good points. At the end of the day, ensuring understanding is the responsibility of the communicator, not the listener. This is what the article is addressing in some aspects, but I think it somewhat shirks responsibility.
Maybe “sorry” wouldn’t sound “defensive or unsure” if everybody understood it simply as a nice gesture rather than as an actual mea culp
I think a better solution would be for one to properly consider the immensely powerful tool of language they use everyday. If someone uses a word or phrase as a colloquialism, one that completely alters its literal meaning, it's their responsibility. It's not fair to simply state 'well I didn't mean it like that,' because you're assuming prior knowledge and then getting frustrated when you misstep. I agree with the advert more than the article in this case. To cease using sorry in that manner is better than trying to make sure everyone understands a new interpretation. A dictionary definition is universal. Sociolects and Idiolects are not.
Also, it's important to keep in mind that sorry is a very powerful word when used the right way. However, there's another context where we hear 'sorry' used somewhat flippantly. Many a time someone will say 'sorry' which, inbetween the lines, roughly translates to: "I'm doing something mildly selfish but don't care enough to explain and/or exhume myself." The original advert actually demonstrates this at the end when the women steals all of the duvet and then says 'sorry'. Though I know that's really meant tongue in cheek, it's an example nonetheless. So one has to be careful not only not to misguidedly betray the literal meaning of a word, but also consider the context where a word might've often been used in similar/different fashion.
Also, I don't know about the US, but in the UK this isn't exclusively a female behavior. Over here, many men will use the word 'sorry' in this context too. I know I have. Perhaps that suggests a more widespread acceptance of its desired meaning.