Question: After setting my coordinates in the Base Point dialog box from the Location in the model options at the bottom, the boxes turn red and the Modify button is greyed out. Why does this happen?

Answer: Based on the Define a base point section of the linked article Base points, all Location in the Model coordinates have a limitation of +/- 10 km (33,000 ft) from the origin. Anything greater than that will have to use the General coordinate system at the top with default settings East coordinate (E) as X, and North coordinate (N) as Y. Z will always represent the Elevation.

As shown above, you are allowed to use a mixture of General and Location in the model coordinates but not both simultaneously as Tekla Structures will compute the numbers into a sum or subtraction. 
 

In some versions, Location in the model options will not turn red. However, having coordinates over 33,000 ft in that section will still cause issues with exported objects, such as dimension or location discrepancies of objects in external 3D viewers.