Consider the last few real-world problems I've solved (or attempted to solve) with math:
If you have a widget (roughly shaped like a cone with the tip chopped off) held at angle a and the widget is tapered at angle b and the tip of the widget has a diameter d, how far is it in x and y from the center of the tip of the widget to the theoretical tip were the taper continued to a point?
If two 14" pizzas feed five people, how many 16" pizzas do you need to feed eleven?
If a gallon of paint covers 400 ft^2 once, how many gallons cover a 12'x36' room with a 9' ceiling twice?
And to counter your claim that it no K-12 math can be fuzzy, if you live in a family-friendly neighborhood of x square miles, how many pieces of candy do you need to be prepared for trick-or-treating children? (This problem could easily be approached by a high school student, has real world application, but is a lot like the kind of interview problems that are often criticized as being irrelevant.)
But even if you feel these problems fit with standardized tests, the more important point is that none of these problems was presented to me the way I am presenting them to you. No one told me that angles a and b and diameter d would be both easily available and sufficient to calculate the necessary x and y. No one told me that comparing square inches would be the best way to determine how much pizza to buy. I was certainly not given multiple choices like a normal standardized test.
The real world mistakes people make with math are often more about knowing how and when to apply math, than doing the math itself. Almost everyone knows that Google can multiply and divide numbers. The real math skill is knowing what numbers to multiply and divide to see how many gallons of paint, or pizzas, or pieces of candy, you need.
Being able to pass a trigonometry test is useless if you can't figure out what to do with your widgets. Likewise for the other examples.
I'm not saying standardized tests have no correlation to real-world math ability. They obviously have some. But it's not exact. And there are lots of real-world situations that are poorly reflected in standardized tests.