Is the ratio between earth's distance from the sun and the speed of light just a coincidence?
It is a co-incidence. The units are what you need to look at, in both the speed of light and the distance of the Sun the units of length are the same (m) (your ratio is $\approx 0.002 s^{-1}$ when you use metres as the unit for the distance to the Sun). The definition of the second is in a sense arbitrary and is a consequence of how we have chosen to sub-divide the day into smaller units of time (there is nothing cosmic in dividing the day into 24 units each subdivided into sixtieths which are again subdivided into sixtieths).

If we had chosen to take as our basic unit of time $1/100000$ of a day rather than $1/86400$ the nice round answer vanishes (if my calculations are right the $\approx 0.002$ becomes $\approx0.0023$)