You are correct that one cannot add information to a base from a shared grid view. However, people can still add information to the base using a shared form view. When someone fills out the form, a new record is created. If you need to associate the information with an existing record, you need to include a linked record field in the form.
Separate bases and a synced table is another good option. This is the preferable option in many cases, especially if users need to be able to edit the new data that they add. (They will not be able to edit the data that was originally synced, only any new fields that are added in the target base.)