tl;dr: Gov't isn't assumed to care about the people's needs "because it's chartered to do so", but rather because they have specific and explicit dependencies on public approval. By contrast, companies have an explicit dependency on their customers (and shareholders). Everyone else and the externalities that they face are completely irrelevant as far as incentive structures for a company.
I'm glad your argument isn't about how the government is supposed to represent The People "at least in theory", I find that one rather funny given how people of my stripe are usually accused of only thinking in theory.
As much as I want to, I can't convince myself of the aforementioned meme wholesale, there must be some counterbalance or we'd all be slaves. But I want people to break out of what at least seems to me to be the notion that while private companies are selfishly motivated, they can invent the institution called government that's free of perverse incentives and selfishness just because they think society needs it to function.
Your point about nationwide approval of the government versus specific approval of companies is a good one. Consider some counterpoints: 1) the politicians need not pander to everyone, only those who care to vote. 2) expanding on the reluctance to bother voting, there's reluctance to be informed, since your vote had miniscule chance of effecting your life. It's known as rational ignorance, Bryan Caplan has a lot to say about it if you're interested in looking it up. In contrast, choosing one company over another always has immediate effect.
A government defines a group of people who tend to have some sort of patriotic emotional bond with each other, much like the emotional bond that ties a family together. This is why people all across America felt the pain of the 9/11 attacks despite the fact that realistically the vast majority of us did not have family members or friends that died in the attack.
At a fundamental level this patriotic bond alone seems to make the majority of governments considerably more altruistic toward their citizens than a company would be towards their customers.
After all the leaders of government are also citizens with that bond of shared country and patriotism that they share with other citizens. In a company there is a much larger "us and them" divide between people in the company and people the company is selling to.
So in this light the grandparent's response of "We the People" though short is pretty meaningful and accurate. Governments tend to have interest in their citizens because of this patriotic bond which says that both the leaders and the ordinary citizens are "We the People".