Unfortunately, this sort of 'we need this evidence and nothing else, even if it doesn't exist' attitude is becoming more and more common.
In my case, my wife worked for a short amount of time in April in the tax year before I became a student. SLC asked for her income during the Academic Year, which was of course, zero. (She didn't claim benefits, and eventually became a full time student herself).
SLC asked for her P60, or August payslip as proof, which of course, anyone who has ever held a job would know you don't have unless you are working in August, or work for the full tax year (or claim certain benefits, when the Jobcentre will issue your P60, which is what you may need to send in your case) They were not happy with her P45.
In the end, we just had to keep re-sending her P45 with a covering letter explaining why the other stuff they asked for didn't exist. Eventually, it was looked at by an assessor with half a brain who "exercised their discretion" in finalizing the grant without the exact evidence they asked for.
In the meantime, it took a complaint, escalated all the way to the independent assessors, before I received anything remotely like an apology or admission of wrongdoing.
If your situation is anything like mine, I can only suggest you keep re-sending the evidence you do have with a letter explaining why you can't provide the evidence they keep asking from you on the phone, and in the meantime, make a formal complaint. Expect to be fobbed off, but keep escalating the complaint until it gets to the independent assessors. It is only likely to change once the IAs start writing in their annual report that SLC need to reexamine the acceptable evidence lists for these sort of problems.
I do have to ask what Comeback suggests would be acceptable proof that you have no taxable income, however. For an example, If you were a full time student who relied entirely on your fiance, with no other work or benefits, what proof from HMRC or your employer (which is all SLC will accept) would you have that you had no taxable income?
Of course, there is another solution. Despite being a Unionist, I sort of hope the people of Scotland will vote YES next Thursday. They can keep the SLC with our compliments, and hopefully the rUK body that replaces them will have slightly more sense.