Moreover, even if the percentage of such people were shockingly high (i.e. over a fraction of a percentage), you would need to conduct a huge survey to distinguish it from error rates on the tests themselves.
Another fun seminar is this one by Prof Pamela Bjorkman at Caltech; it's useful to watch the slides with at least one eyeball so not for dog-walking. https://www.youtube.com/watch?v=OBcc_dk9Q9U
https://www.nature.com/articles/s41591-020-0819-2
I can’t find any research suggesting that patients (symptomatic of not) are recovering in some other way.
And in any case, recovery implies some form of immunity, either innate or adaptive. The virus doesn’t just give up after 14 days.
My layman understanding is that a vaccine relies on the body creating antibodies.
But that doesn't mean that it is impossible to create a vaccine: this problem exists already for successful vaccines. For example, the Hepatitis B vaccine has a relatively high failure rate, but is still provides immunity 90+% of the time. It just means that some smallish percentage of the people you vaccinate aren't actually contributing to population immunity.
See below for more info:
https://en.wikipedia.org/wiki/B_cell
https://en.wikipedia.org/wiki/Memory_B_cell
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3760154/ --> this one is particularly good. A lot of good info in here on how vaccination and "memory" interact.
https://www.sciencedirect.com/science/article/pii/S0264410X0...
EDIT: this one covers the major routes of vaccination failure --> https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4962729/#!po=60...