I've been pretty much obsessed with the basic step for the past year and one of the things I've found is that there are many many ways of dancing on the same timing.
The following is my attempt to give an answer to your question, which is based on my experiences, experiments and feeling. I'm not a teacher or an expert, and this is full of conjecture!
Now I think of dancing "on time" and "on rhythm" as being different. In this wording, I'm using timing in a metronomic sense and thinking of rhythm as something that has "texture" and "lumps". A lot of the people that I've danced with in the UK, and most of the time myself too, feel metronomic in the sense that each part of their basic step seems to have the same emphasis, i.e., it's "rhythmically flat" or regular.
I've seen a video on the Baso.tv and Santo Rico studio site where Tomas talks about having a "bounce" in the basic step, and he goes on to say to try and feel the space between the 3 and the 5, and the 7 and the 1. If you're a subscriber it's called: "Santo Rico Shines - Advanced Variations of the Basic Step"
Taking this concept a bit further, when I think of dancing to the conga, breaking on 2, there is a "light and shade" that I perceive in the basic step and the effect is like that of slowing down time. To exaggerate, it feels like 123 fiiiiive 67, which is probably practically accomplished by pushing the recovery step forward onto 4& and travelling more through the recovery steps and treating the break steps as changes of direction.
At the moment this is what gives me the most pleasure, when dancing to say, typical 70s Fania.