In the US, you have protections if you have a union contract. Otherwise, you pretty much need to be considered a protected class (varies by state), and your sacking was related to your class status.
Forget about the legal risks; how does that even work? If I don't think my coworker is doing a good job, am I supposed to secretly whip up enough votes to have them fired?
In my experience, it generally becomes clear to everyone if someone is really not working out, and it's already been the subject of hushed conversation.
If you need to "whip up votes", this will say more about you than the person you think isn't doing a good job.
Borderline cases are trickier, but they are for managers too.
The only time that a "single boss" would know better than the team would be if the single boss was as knowledgeable about the development process as the team was, and knew that the team was, for some reason, cooking up a conspiracy to fire a certain employee who didn't deserve it. Probably pretty rare, especially compared to the number of people who get let go because they just didn't click with their supervisor.
And of course there always is a single boss even if this fact is hidden; in the case of Valve it's presumably gaben, who owns the majority of the company and must presumably be the final arbiter of everything that happens.
I can only assume that the actual firing process involves a lot of hushed talking followed by an approach to gaben followed by a discussion followed by a "sorry, bye".
One could in fact suggest that the flat management structure only works when there is exactly one clear owner of the company. Everyone can pretend that everyone gets a say, when it's clear to everyone who really has the final say.
Wonder if that kind of 'firing' ends up in court?