That being said, like you I am curious for more details! It does seem a little strange on the face of it.
I think most voters in democratic systems conflate the two and miss this in it's entirety.
Power rests 100% with parliament.
You ask "why?". It's a good question. The system is hard to defend logically, but it is respected nonetheless.
The Brexit situation is one good example why. They posed the wrong question and arrived at an answer the majority of both the voters and the parliament are already deeply unhappy with...
If I wanted to grab power and rule as a dictator, I would hold referendums every month. You just wouldn't like the questions or the rules...
I think they're more democratic, pretty much by definition.
The point you're making is that they're not good.
To enhance democracy, referendums need certain precise conditions, which are hard or impractical to achieve. For example: Who decides what goes on the ballot?
What do you do if too many issues make it on the ballot, such that the voters and the election staff (or volunteers in most cases) get exhausted and can't effectively participate? How should campaign financing be controlled? How are democratic norms enforced against referendums if necessary?
Another interesting issue arises when voters decide on the rights of those who are not allowed to vote. Mostly immigrants today. But guess how Switzerland became the last democratic country in Western Europe to get full voting rights for women...
Firstly, the goal of a non-binding referendum is to gather public opinion.
Secondly, the outcome of the referendum was respected for 13 years.
Curious - why is Left Hand Traffic better than Right Hand Traffic?