I was a mathematician, and now work in finance (systematic trading). I've found a reasonable negative filter is A jar has 1000 coins, of which 999 are fair and 1 is double headed. Pick a coin at random, and toss it 10 times. Given that you see 10 heads, what is the probability that the next toss of that coin is also a head? That tests their ability to turn a problem into mathematics, and some very basic conditional p…
The funny thing is, I imagine I'd fail this, and a lot of other "interview" questions. (Not fizzbuzz incidentally :P) Why? Because my brain just doesn't seem to work in the way people expect "experts" brains to work in our world of tests/qualifications. Now for context, I don't consider my self some wishy washy "Oh I have a different KIND of intelligence" making-excuses dumb as nails nancy. I've worked several years…
The negative sign is your stubborn conviction about the lack of value of rote memorization.
The stereotypical "rote learner" you describe in your before-last paragraph is just as one-sided as the opposite.
Of course neither extremes really exist and you probably have rote-memorized more things than you realize. You don't work out everything from scratch every time you encounter a medium hard problem.
Unless you actually do, in which case someone reasonably clever who does not stubbornly refuse to learn a few formulas will beat you by speed. Which is a reason to hire them over you.
That's the the point. You may be very smart and capable doing it this way, but learning a few basics (such as Bayes, in the context of statistics) doesn't really cost you anything. Memorizing a few things isn't hard. You won't actually run into problems like "erroneous thinking" because you're smart enough and knowing the conditions under which something holds is easy enough when you understand the thing. Additionally you get the knowledge when a particular important theorem does not hold, which is higher level knowledge that you just can't get when you reason from scratch every time (positive vs negative knowledge).
Memorizing a few of the basic important theorems and formulas in your field is such low-hanging fruit to improve yourself that a potential employer might ask why you're not doing it, even if you're so very capable without doing it.
Finally, there's communication with your peers. Maybe you can figure that stuff out by yourself easily, but when your colleagues say "ah, so we just use Bayes and poof", you'll be lagging behind figuring that out, and in reverse when you do these things from scratch, I'm assuming you'll be doing them much quicker, speeding through your ad hoc methods, leaving your team mates confused and wondering "why don't he just use Bayes?" (which may or may not be what you are in fact doing, but you lack the knowledge to tell them as much).
I'm sure you do a very good job at what you're doing now, the way you're doing it. I'm just pointing out that there are various well-justified reasons why employers can be wary of your refusal to memorize some basic field-knowledge, even when you're perfectly capable figuring out that stuff when you need it.