FWIW, here are specific rule references:
If the string touches the physical depiction of a terrain obstacle or hindrance in an intervening hex, that LOS is blocked [23.2] or hindered [23.3], respectively.
The "physical depiction" means the drawing/art itself of the terrain (building or trees etc).
Note that this says it works this way, regardless whether LOS is blocked or hindered.
A Smoke hindrance  is considered to fill the entirety of the hex that its marker occupies, including its hexsides. In other words, a LOS traced through any portion of a hex containing Smoke – including directly along one of its hexsides – is hindered by that marker.
I.e. smoke fills its whole hex.