Well, Yes and No. It's only half the story but it sometimes gets billed as the whole story. And that's one reason why "the country" is often badly run.
The other half of the story is that democracy is about having influence over the legislation under which you live. This is obvious in a country like Switzerland which - much to the embarassment of the rest of Europe - makes frequent use of Referenda. People vote on whether they want to live under such and such a legislative proposal and their votes are binding. Ouch!
In the UK, Parliament which is supposed to be a legislature is pretty unfit for that purpose. One half of the Parliament - the House of Lords - is an unelected fraternity of lobbyists paid to insert clauses into legislation which favour those who have paid for the clauses to be inserted. Let's not beat about the bush. People in the UK would live under better legislation if the House of Lords was simply abolished. It would save money too.
The House of Commons, the popular chamber, conducts its business in such a way as to make it difficult to get any legislation - good or bad - onto the books. It spends a lot of time on holiday. It spends a lot of time in schoolboy debates (sorry, they are schoolboy debates even if some of the boys are girls). It struggles to pass legislation in the time left so that important pieces of legislation often don't make it before they are timed out. It is at the mercy of government whim so that legislation which has been promised can simply be withdrawn and legislation no one had previously thought about can be rushed through. Ordinary members have little scope to introduce legislation themselves - everything depends on the government, "the people elected to run the country".
If someone inspected the House of Commons in terms of its efficiency in passing legislation, it would fail the inspection. It would fail even more if you assessed legislation in terms of its clarity or simplicity - let's say, the ability of a court or a jury to interpret it without too much difficulty.
The media play a very large part in ensuring that we think about democracy in terms of Who Should Run the Country: cuddly Boris or nerdy Ed? A re-balancing of political debate would involve giving much more emphasis to such questions as , What old legislation would you like to see removed from the statute books? What new legislation would make the country a better place in which to live?
Remarkably, these two questions are ones which are rarely asked. Except in Switzerland.