You right, but since we are talking about immortality here simply elongating the sequence won't do. We are speculating here about the ultimate consequences of this technology, in case that the whole sci fi dystopia wasn't a big clue
I don't necessarily think that genetic modification will cause mutations but we have no research whatsoever on adverse effects.
Genetic modification may not cause mutations, but ultraviolet light and oxygen sure will!
To truly have immortality you need either: a cure for cancer, or true AI (or to be specific, the ability to download a human brain and optionally and ideally transfer it into a new living host e.g. clone)
Otherwise no amount of senescence prevention will prevent death.