Switzerland is certainly democratic, because voters can directly vote for laws. Some countries and states do have provisions to that effect, but with more restrictions and less often used.
The US is actually more democratic than e.g. Germany, because the president is elected by the people (though indirectly), not by parliament. Therefore a political oligarchy could be prevented, because the majority in parliament and the president can check on each other, and the president is more accountable to the voters than to parliament.
Generally there is a sliding scale of course, but the less directly officials are elected, the less democratic a country is. A common example would be a soviet (engl. "council") republic, which isn't considered democratic at all, even though it has tons of elections: Each factory/town/village elects a local workers's council, which in turn elects a county council, which elects a regional council, which elects a state council, which elects a national council, which elects the council of ministers, which elects the chairman. Tons of filters that make absolutely certain that the will of the party and state always supercedes the will of the people.
> The US is actually more democratic than e.g. Germany, because the president is elected by the people
The German president is mainly a figurehead with limited power. The office was stripped down after WWII.
The real power lies with the ministers, who can issue absolute orders that have to be obeyed without question. One of many results is that German prosecutors cannot be trusted with issuing EU wide arrest warrants and had the ability stripped from them the moment it was challenged in court.
I was comparing the USian president to the German chancellor. Both head up the government made up of ministers they appoint. It's only the name that is different, and the order in protocol. The USian president is first and head of state in protocol order, the German chancellor is third after the German federal president and the president of the Bundestag (one chamber of parliament).
Sorry for my being imprecise here, Germans tend to skip their own president(s) because, as you correctly state, they are mostly unimportant figureheads.
The US is actually more democratic than e.g. Germany, because the president is elected by the people (though indirectly), not by parliament. Therefore a political oligarchy could be prevented, because the majority in parliament and the president can check on each other, and the president is more accountable to the voters than to parliament.
Generally there is a sliding scale of course, but the less directly officials are elected, the less democratic a country is. A common example would be a soviet (engl. "council") republic, which isn't considered democratic at all, even though it has tons of elections: Each factory/town/village elects a local workers's council, which in turn elects a county council, which elects a regional council, which elects a state council, which elects a national council, which elects the council of ministers, which elects the chairman. Tons of filters that make absolutely certain that the will of the party and state always supercedes the will of the people.