The parent was probably confusing RNA with adenovirus which IIUC does deliver DNA that integrates itself into the genome. There are dozens of COVID vaccines under development right. Many of them are in fact DNA vaccines. To date they've only been approved for vaccinating dogs of rabies. The mRNA vaccines that companies like Pfizer are making have the advantage of not permanently changing the DNA in the target cells. Even with DNA vaccine it's not the end of the world. For example, herpes simplex (cold sores) is an example of a natural virus that integrates itself in the DNA. But it's localized and it's not something that your children are going to inherit. Another interesting fact is that the Pfizer mRNA vaccine and others are delivered using lipid nanobots rather than adenovirus which I think is cool. But DNA vaccines have even potentially cooler applications since it means the medical field might for once be able to offer cures to illnesses, rather than charging you for a pill every day.