You're assuming that "math problems" is a well-defined set of problems. But depending on what you want to test/teach, there's also going to be different problems that students will do well on.

As an example: do you consider solving 579×46 quickly a "math problem"? I will solve it (relatively) quickly, since I was thought how to solve that exact problem algorithmicaly.

But if you hadn't thaught that algorithm (you could argue that nowadays we have calculators for this) then it would probably take you a bit longer to derive some form of this algorithm. But it doesn't necessarily imply that you're bad at math, just that you have not practiced this exact task before.

In my experience, doing really well in tests requires more adaption to the tasks of the tests than actual understanding. Most tests are limited on time, and stress does not exactly help you to deal creatively with completely new tasks.

Note that I don't want to say that teaching algorithms is bad. It surely helps to do some basic calculation without having to think much about it. I just want to point out that the tests are often testing a specific understanding of math, and different teaching methods often also differ in their goal of what they want students to learn well.