ALWAYS/NEVER has a lot to do with attracting clicks. You ALWAYS see headlines like this getting voted up, but NEVER see articles titled, "It may usually be a good idea to not negotiate piecemeal," getting much traction.
Your latter claim is debatable but isn't wrong. I would just say that if one is willing and capable of adapting and adjusting to the situation, that you're going to be at least competitive with if not ahead of most people with an inflexible strategy. Only in solved games does the 'fixed' game theory optimal strategy beat anyone who deviates.
I agree with that headlines must be catchy. But I talk about the article and not about the headline. If after clicking I would've read a great, meaningful article, which analyses the pros and cons of bargaining peau a peau and/or comparing both strategies with each other, giving the reader a better sense of when to use which, I would've silently "upped" the article. But the text itself is flawed with that idea, that there is this one strategy that beats all the others and is always correct. At least that is how I understand the authors point. And that is also what I can't agree with. That thinking itself leads to bad results, because after making mistakes (and everybody does) you think "oh gee, I did the wrong strategy again, which else can I choose?", which won't get you anywhere.
Your latter claim is debatable but isn't wrong. I would just say that if one is willing and capable of adapting and adjusting to the situation, that you're going to be at least competitive with if not ahead of most people with an inflexible strategy. Only in solved games does the 'fixed' game theory optimal strategy beat anyone who deviates.