Being interested in democracy means using your vote (or making a decision to abstain). Not bothering to vote is incompatible with the declared interest in democracy.
That's a strawman.
Plenty of people are not interested in all or part of a democratic system, but appreciate that it exists, and that it provides channels through which they can influence the way they are governed, if they deem it necessary.
Most people don't know the differences between the town council and their local authority; they have no idea who their councillors are; they might not even know which party has control.
For what it's worth, I voted in the local elections held this year, have voted in general elections, and have even met up with my local MP to discuss financial reform.
Furthermore, the idea of a representative democracy is that you elect people to work on your behalf. You do so because it's a full time job to stay abreast about all political issues. Even if I knew the names of all my local councillors, knowing their names doesn't give me any insight into the decisions being made. Most of us have a limited range of interests, I could tell you about political activity I'm interested in, would that satisfy you that I'm paying attention?
Without looking them up are you able to name all your local councillors?