Fences (and similar) you can walk on both sides of will be made of tiles on the building layer (the bottom part you can't walk through) and the tiles on the front layer (the part on top that renders over you when you come from above). Grass goes in front of building layers (you need it to, for when you are planting it in
front of the fence!)
If you turn off your mods and walk to the bus stop or into town and plant grass all along the fence (or in front of trees or trash cans or etc for that matter), it will clip through the bottom. It's usually covered up by front tiles in inaccessible-southerly areas, but if the player can stand in front of/under it, that tile will go on top of them -- which isn't usually the look you want, hehe.
Without using additional mods to give you more map flexibility, most map makers are choosing between left (vanilla) and right (front) or avoiding it altogether via inaccessible areas and carefully placed decor. Or just not having built-ins and leaving that for players, of course :)
Since the right option always sucks even if people don't plant grass, left is probably most common. If they're willing to add more dependencies for their map than just Content Patcher, they can require another mod that lets them add more map layers, which is the only way I know of to get to happy middle at this time. I don't think it's usually in the forefront of anyone's mind, though, and you can often find little layering issues here and there even without more dynamic elements like grass and trees :D
As a player I don't think there's anything you can do except trim your grass and/or use creative placement of decor (especially paths, to make a buffer between grass-OK areas and places it would clip hideously), but it's not a difficult map edit if you want to take a stab at option B!