I'm not a bit clear about what you're objecting to. The test, according to the document it's embedded in, was administered to students in training to become mathematics teachers---though I didn't read it carefully enough to figure out at what level.. I certainly want those who teach mathematics to be able to answer these questions appropriately, though the questions about "rigor" may be poorly formed.
The aim of the test seems to be to test whether students can differentiate good arguments from bad arguments. The ability to do so is important, because proof is central to mathematics. Those who can't distinguish between good argument and bad argument certainly ought not to be teaching mathematics. Even those who *can* do so but don't understand that proof is central to mathematics (and this includes many who mistakenly think that they want to major in mathematics) ought not to teach mathematics. (And the reason, I suspect, that the latter category includes so many who discover too late that they don't really want to study mathematics, is that too many of them make it through to become mathematics teachers. Allegedly, anyway.)
-- --Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State College of Denver