replanting a tree
It is okay to plant another tree. Planting has more to do with the amount of large and small roots left in the ground. If you had the stump ground out to 10-12 inches down, there is still lots of wood below that and it could be dense. Stump grinding grinds the stump, not all the roots that radiated away from the stump. It could take a long while for them to break down.
Also, if there is any stump grindings or wood chips in the planting hole, they take nitrogen from the soil as they decompose and the soil will settle where they have ground out the stumps.
If all roots were removed, you can plant nearby but not generally recommended to plant in the same spot unless you have space constraints. You need ample growing/rooting space and good drainage. Select an area at least several feet away from the original location to plant.