No it does NOT. Not apologizing if you're wrong makes you a douchebag. There might be something you missed and therefore you want to correct yourself. It happens all the time - no big deal in an apology.
PS - This is a general comment on tendering apologies and has got nothing to do with the OP.
Experimental evidence seems to indicate otherwise[0]. Specifically outside observers punish insincerity (coerced or feigned apologies) more harshly than insensitivity (no apology) and in far greater degree than the wronged party punishes either.
So if there are third parties present, the best strategy is not to apologize unless you are fairly certain it will be viewed as sincere. In the absence of a 3rd party, apology is the winning strategy regardless of sincerity.
I found it interesting that the recipient of the apology is made to feel better not because the wrongdoer cares enough to apologize but because it is an opportunity to be seen by others and affirm one's self-image as magnanimous and gracious by accepting. We are such odd creatures.
The best course of action is to express regret without accepting responsibility unless you actually believe you were at fault.
Aw man! You have made it sound so complicated. I would say if you are wrong apologize; if not do not. I don't think your apology should be viewed as something against you. If it is; I think you are are working for the wrong organization.
I hope there's at least a tinge of joking in there. If you do something wrong you should apologise. If you rear end someone or walk into them while texting apologising is the right thing to do. I do agree with the point of the article though. If you have an opinion and you can justify it then there's nothing at all to apologise for.
No, it makes you look intelligent and human. Apologizing at the end of an article like this only shows that there are higher powers at play trying to shush you up.
PS - This is a general comment on tendering apologies and has got nothing to do with the OP.