How precise do models need to be for 3D printing?
It depends on what you're working on. If you're producing mechanical/functional parts (even if that just means having to connect to one another or to some non-printed part), 3 mm (0.3 cm) error is almost surely going to prevent them from working. Even 0.3 mm error might be a problem.

If you're doing standalone prints that don't have to interface with anything else, e.g. art, non-articulated figurines, etc., then it becomes just a question of what's visually acceptable, and that's a matter both of scale and of the detail level you want. For typical tabletop-RPG scale, for example, most of the acutal visual features are going to be smaller than 3 mm, so that much error is not going to work out. It might work for large busts, though.

In any case, I would recommend trying to solve the underlying problem. Either change your grid snap, or work at a larger scale and just scale down the final model.