haha I can relate

Welcome to the world of teaching children

That's not at all unusual

No she's for sure not tone deaf!

But she might have felt tested and as soon as she spots something like this, she might have tended to tense up inside and she might have only been able to think "what the heck, what the heck does that teacher expect from me now...I need to figure it out, for god's sake, I need to make no mistake, omg.." and so on, and of course, nothing works anymore!
The solution: you might want to lead her indirectly! No "tests" of single pitches or melodies, or singing along as far it requires a sort of "being exposed"-feeling! No tests at all, except those tests who seem very fun to them anyway!

I have given up on those sort of "feeling-exposed-tests"(aka feeling under pressure) years, even decades ago, as they're worth exactly nothing!! You will anyway have a true impression of the student after a few lessons, without any "tests"
Try to get her into some sort of "flow", be it through adressing her through one of her favorite songs or through something she can already play, or some games on the keys, or whatever. To fit the exact pitch at singing along may take a while, and you have to just ignore if she's out of tune, or singing a fourth below or above or whatever. In all probability she IS able to follow the melody in
some sort of way, and that's where you have to chime in, and support her!

After all it's about partnership and you will have to find the common level where the partnership of your two individuals is possible

P.S. of course later on you might get into a situation where you need to prepare a student for "being-exposed-tests" but as you will in all probability have guided such a student for years already, you might find also the way to prepare him for those, according to your experience and partnership with that particular student.