The counterpoint to this is that in order to motivate large groups of people to get stuff done, you need to be 'involved.' A good leader cannot be someone who says "we're above all of this" -- they have to be involved, they have to influence, and they use their influence to productive ends.
You actually cannot be solution oriented without politics. If you are "not involved in politics," that means that politics is involved with you, and you'll be forced to go wherever it lands, instead of attempting to influence the outcome.
It turns out in the end, we are solving problems for real people, and so all the messiness of real people: the pettiness, the tribal nature, the bickering, the facts-bent-to-justify-feelings... That's in the problem domain.
(For software engineers in particular, who can trend towards wanting to think of themselves as little logic-machines divorced from that kind of behavior: I also think it's a good exercise to keep that stuff in-scope because we are not immune to our own humanity, and recognizing when others are being tribal and petty makes it easier to recognize it in ourselves.)
The problem is way more "involved in what exactly?" than whether people should be involved or not.
The GP is right that people tend to name stuff as "politics" when there is no external goal. And getting involved on those is just bad.
But also, the GP is wrong if you go with the formal definition for that word, like you are doing.
If you're not involving people in the problem solving, you're probably solving the wrong problem.