Doesn't have to be a zombie apocalypse to make it a rational action. Could simply be trying to escape/hide from an army/militia know for being vicious, trying to outrun a nasty plague being spread by perfectly function carriers, running from That which man was not meant to know, trying to survive stranded on an alien world with hostile flora and fauna (think Predators or other sci-fi).
All have the same underlying threat, something scary wants to kill you. You know you need to act to outrun it. Someone is preventing you from acting. Do you try to negotiate with what you instinctively feel is a fatally flawed premise in a life or death secnario, or do you remove said obstacle to your survival.
This is all good drama and story. You can roleplay the psychological aspect of having to make these kinds of choices, and I personally think a Walking Dead game would be a great place to have a sanity/humanity mechanic, like the Jenga Tower thing. As you shed your humanity, you get closer to going over the edge. Once you've gone so far over (your Jenga tower falls), your character is now an NPC, whether psychologically broken and useless and traumatized, or becomes an antognist.
Naturally, it'd take a consistent pattern of tossing aside humanity to completely lose it.
Given that the show Walking Dead is really a drama/soap opera, all of this conflict is in fact "good" roleplaying. Except for the part where you take action against the party.
The point in drama is a lot of talking and arguing. Only at extreme points does it come to unretractable action (like throwing a character to the zombies).
So, sitting in the cooler, the party should be arguing and having that throw the weak ones as bait discussion. That doesn't mean you actually do it. Out of character, you take a final vote, and then in-character, your PC reluctantly follows along (so as to maintain meta-game cohesion).
One of the initial problems I see with the OP, is certain expectations of high-octane action, that isn't part of the initial session.
Frankly, in the beginning, no matter where the PCs go, you'll find it has an infection rampant. No matter where you hide out, the horde will finally surround it. The first act of any zombie story is the protagonists being off-guard and on the run and overwhelmed.
If you survive that (and play through it) and finally get to someplace safe, then you build up and go on the offensive or are prepared to mount a proper defense from an attack.
But until then, your dreams of chainsaw cars, mowing with Combines are just dreams because your PC won't likely have a chance to locate the equipment and prepare the attack.