DNA stability is quite high. To the point where there is actually a movement to get scientists to stop freezing DNA for long term storage because it uses large amounts of energy for no reason.
You are seriously mistaken. At abient temperature, DNA is very stable. Even in an active environment as a human, it keeps quite stable for about 100 years. Isolated for multiple millenia. It is the reason we can sequence neanderthals etc nowadays. It wont be stable for millions of years but with some redundancy you could easily make it to 100.000