We would have "true-and-I-can-prove-it" and "true-and-I-can't-prove-it." I'd be surprised if given those two categories there would be many people who wouldn't elevate the testable statements above the untestable one in "truthiness."

Where would mathematical statements fit in this classification of yours? They can be proven, but many of them can't tested and even for the ones that can be tested the proof is generally considered better evidence than the test.

In fact, you are implicitly relying on a large untested (and mostly untestable) framework to describe the relationship between whatever sense input constitutes the result of one of your tests, and the proposition being tested.