No, you can explode in any place and still get the DNA. The reason why people try to explode on Fleet is just the daily to infect 10 players. Which is pointless in my opinion - i've just completed this daily and got... rakghoul vaccine x5 as a reward -.-
So the fastest way to farm the DNA by being infected is:
Go to Tatooine daily area, get yourself infected, find a good safe spot and afk 10 minutes until your debuff transformes into "Fevered". When that happens don't wait anymore for the explosion, just let something kill you. As an imperial, when there were no republic players around, i just went to their blockpost (pretty close to the daily area) and charged into the champion type guards. Like this you are saving time waiting for the full process.
Bah, slow posting is slow.