It does sound rather like in a football game, electing to kick instead of receive on winning the coin toss.
Except there is an weather related situation where it is rational to do that.
That is a really unusual decision.
Because Martin pitched better. That’s just what the rulebook says; it is supposed to go to the reliver who was judged to be “the most effective.” Martin was more effective. The official scorer really had no other choice.
It’s clear that wins aren’t a statistic. Stats are supposed to represent objective data. “Wins” then are as useful as measuring “quality starts” or “highlight plays”.
I wonder when they’ll start quoting every player’s “coolness factor”? 
Well, in probably 98% of the cases, they are an objective (if fairly useless) stat. It’s the odd corner-case like this one in which it’s subjective.
That said, as the sport evolves, and as starting pitchers increasingly pitch less than the five-inning minimum to qualify for the win, the stat is becoming at least somewhat less objective, overall.
Well, sure, but even if we credit the entire defense to the pitcher, that’s still only half the game. If one team allows only a single run all game, while scoring none of their own, and another team allows eight runs, but scores nine, which pitcher is deserving of more credit?
I believe you are correct.
Responding to the OP, I’ll often check after a play to see if it was called a hit or an error. It’s extremely rare that I disagree with the call. I can’t even remember the last time I think they got it wrong.
And as I am sure you are aware, hit/error calls can be changed after the fact. I rarely watch sports anymore but many years ago I was watching a Dodger game and the scorer made such a bad call the Vin Scully burst out laughing and the cameras showed the fielders looking up at the where the scorer sat with confused expressions. The call was quickly changed.
I disagree with your definition of “statistic” but agree wins aren’t a good one in any case.
Baseball has a number of stats that have a subjective element - errors, passed balls versus wild pitches, some sacrifice hits, etc. Defensive Indifference has no objective criteria and I’ve seen it wipe out a stolen base when it was clearly not the correct call. I don’t like them.
Quality Starts are entirely objective, though.