>>The short answer is similarly to how dinosaur DNA survived in bugs found in amber...
Nope.
http://www.sci-news.com/paleontology/science-dinosaur-dna-amber-01383.html
Don’t trust Hollywood movies to give you accurate, hard science.
I only mentioned the Amber DNA as a humorous pull on your chain. I'll remember the sarcasm and/or irony tag next time.
Were you aware of the DNA work done on the Kennowick Man bones? Successful results for $400 when done by the local officials. Fedzilla bureau-scientist spent some $10,000 and got invalid results.