Not at all and expert, but I think the idea of reprogramming is wrong, as it implies the vaccine is editing DNA (source code).
mRNA vaccines are more analogous to temporarily running a subroutine.
mRNA vaccines are more analogous to temporarily running a subroutine.
But I guess the parent comment was using “reprogramming our bodies into vaccine factories” as a hand-waving description rather than a technically precise term. And that description is then roughly correct: with RNA vaccines, it is correct to say that our bodies are being triggered to produce the actual “vaccine” themselves; namely (at least in one type of RNA vaccine), the body’s cells are translating the injected mRNA to produce antigens, which is what a conventional vaccine contains, and which, in turn, produces an immune response.
But, "literally" actually has a specific meaning in english, and it's not always to be literal.