Not a couple of Hundred meters....Checkov reports 4,000 meters and the Excelsior is just clearing the Station's perimeter.
In any case the whole warping too close to planets has to the do with magnetic fields. It' not that i'ts impossible it'st that it's dangerous.
In the book Prime Directive the Enterprise is destroy above a prewarp society that discovered them and launched nuclear war heads at the ship. The empluse engines were disabled and in order to get away because they were sinking into the atmosphere they warped.
The result was that the fields caught a field line from the planet and ripped a nacelle off a strut. In another book it was possible to warp out of earth orbit and the solarsystem becauce of accurate magnetic field fore casting as well as solar magnetic field forecasting which are far more erractic.