The LNP disguises the mRNA to allow it to pass through the cell membrane and not be attacked by the immune system. So the mRNA actually does infiltrate the cell wall, and bypasses the immune system. Just a straight injection of mRNA would get wiped out by the immune system immediately, that's why the LNP was used.

To alter the DNA there would need to be reverse transcription which may or may not occur. Some studies have shown it did occur. ¯\_(ツ)_/¯