I don't know what the instructions for enumerators was in 1790, but in 1850, it says:
"Indians not taxed are not to be enumerated in this or any other schedule."

In 1860:
"5. Indians.-- Indians not taxed are not to be enumerated. The families of Indians who have renounced tribal rule, and who under State or Territorial laws exercise the rights of citizens, are to be enumerated. In all such cases write "Ind." opposite their names, in column 6, under heading "Color."

When someone was acknowledged as existing in the household by being called "other free"...was that enumerating them?
If they were considered citizens, they would be paying taxes, wouldn't they? And then would'nt they be enumerated by name?