Not knowing the structure or content of your table, all I can say is that on the surface, what you say is absolutely true. A table CAN stand alone. Maybe the question that should be asked instead is:
"Should a table stand alone?"
The answer to this would depend on the content of the table.
If a table is structured so that there will be no duplicated data, then it is possible that it could stand alone.
If a table is structured so that there will be duplicated data, then splitting the table to eliminate the duplications will not only make it more normalized, but be more efficient as well.
As an example, if each record contains a customer Name, then the potential for a data entry error exists, and will only increase as time goes by. Adding a customer information table, and using the customer ID instead of the name, will assure that the correct customer information is being used.