It doesn't matter if they can cure it or not, they turn up and you have taken the responsibility away from the players. The national guard can surround the place and drop a themobaric bomb on it if it looks like it will go out of control. The players can hand everything over to the authorities and get on with their boring and ordinary lives, which would not make for a good campaign.
You're assuming that the CDC even shows up. This doesn't have to happen at all.
Why? According to the set up information no outbreak has even happened yet so there are no zombies.
If you read the scenario I outlined in my original post you'll see that I considered this and gave multiple examples of how the outbreak occurs.
Which is fair enough but then the campaign is about avoiding / fighting the US administration and not fighting zombies its not a Resident Evil game anymore.
This doesn't have to be the case. Again, the CDC doesn't have to show up, and using the police as an obstacle would simply add another layer to the campaign beyond fighting zombies. Also, as stated in my original post, one of the examples describes how the police station could become ground zero for the outbreak. I doubt the police would call the CDC in since they're all zombies by that point.
Right so your character will want to not use normal legal channels (even though he's a coffee shop owner, not Batman) and will instead use vigilante justice and become a wanted felon, and then again the campaign changes its mood and themes.
Ummm, remember that this is a game. Umbrella is a ruthless corporation with more than enough connections to ruin your life in game terms. I can think of half a dozen movies and TV shows that use this to isolate the main character quite successfully from using "normal legal channels." To name three, The Fugutive (TV Show and Movie), First Wave and Minority Report. All three shows had a main character framed for murder. They therefore couldn't use "normal legal channels."
Yes, this does change the theme some, but why not go a little beyond the potboiler RE setting and expand beyond it. Also, this doesn't completely eliminate the zombie killing and actually would give rise to plenty of additional plot hooks (including the kidnapping of family members to keep your mouth shut.).
Finally, read my original post gain. You'll see that was a rough outline of a potential scenario with some examples of possibilities for plot lines. It was meant for inspiration, to get Angelsboi thinking about the adventure and which way he wanted go with it. In fact I told him in the post to use what he wants and discard the rest.