As you said, closer isn't a measure of only distance it is also a measure of time. If the transit system can isn't too far to walk to, runs often enough that people don't worry about when it comes, and doesn't waste time going places the rider don't want to go: people will take it. When transit is inconvenient to get to, doesn't run when/were individuals want to go, or takes too long to get there: people won't take it.
Fixing that isn't easy though. Roads/streets need to be designed for transit. Enough people need to ride that the system isn't mostly empty. It needs to go more or less direct routes to where people want to go, not take long detours to other destinations. Only the middle depends on density at all, if you fail the other two density won't give your transit systems many riders. Pass the other two and you can still get a lot of riders despite not being very dense.