I haven't read the paper cited, but I would almost guarantee that the mRNA and dna in this study are both in vitro, meaning, on a petri dish, not within a cell.

RNA is notoriously unstable, and has a very short half life. If you were to swallow a bunch of this RNA from the article, very little would even touch your various cells' dna. Our bodies are full of enzymes that destroy RNA, as it is typically associated with viruses, which our body knows are bad.

I could get into more, but mRNA is NOT bad. You can find lots of articles where it may seem scary, but those are all highly controlled experiments whose results are next to impossible to replicate in the body.