So, by the very logic used by MDHHS to arrive at the conclusion that COVID-19 vaccines cannot alter human DNA, we must conclude that the Janssen vaccine potentially can do so.
But what about the mRNA vaccines? Well, in this case, the logic used by MDHHS is a non sequitur fallacy.
It is does not logically follow from the premise that mRNA does not enter the cell nucleus that therefore it cannot be incorporated into host DNA.
In fact, there is a known biological mechanism by which foreign RNA can and does incorporate into host DNA. It is known as "reverse transcription". In brief, the RNA is reverse transcribed into DNA, which can then enter the cell nucleus and become incorporated into the host DNA.
You can read more about how this works in
this Encyclopedia Britannica article.
Note that this is the process used in the "PCR" tests being used to diagnose COVID-19. These RT-qPCR tests reverse transcribe SARS-CoV-2 (the coronavirus that causes COVID-19) RNA into DNA for amplification.
It is also the process by which RNA viruses can incorporate their genetic information into host DNA. In fact, a significant proportion of our own DNA is
viral in origin.
Moreover, there are studies providing evidence that SARS-CoV-2, which is an RNA virus, can incorporate its genetic information into human DNA through this process of reverse transcription. See
here and
here.
Thus, it is theoretically possible that mRNA from the vaccines could similarly be incorporated through reverse transcription into host DNA.
The uncertainty about this is expressed in an
article published in the Journal of the American Medical Association, JAMA, on September 3, 2020. As noted by the author: