DNA integration associated with the modified mRNA shots is an issue. It is an issue because cancer. Let’s break it down like a nuclear membrane during mitosis. When cells divide, their nuclear membrane has to break down and be re-formed as part of DNA copying and distribution to daughter cells.1 Any foreign DNA that might have found its way into the cell could get packaged into the nucleus when the nuclear membranes reform. It could also get into the nucleus via transport by nuclear location sequences like SV40.2

Getting foreign into nucleus: not a problem.