@pendeansomething very strange happens here.
If I try to select anything by clicking outsite of the table, like shown below, nothing is selected:

If I try to click anywhere inside the table, it selects the cell. Then, I can click again and use a rectangle selection to select multiple cells, open properties, and make the change you suggested, but nothing changed again! If I select a cell, after making that change, and check its properties, I can see that the cell is set to have clour defined by layer, but that setting doesn't affect the text inside the cell at all! It's like the text inside the cells are using settings that overwrites whatever settings I pick for the cell itself. It seems like the cell setting is different from the settings of the content inside the cell. Not sure if you could understand that explanation here. It's just too bizzar.
The text inside all cells, except on the first row, are invisible on model space, but when hover the mouse over it, the text is then displayed:

I selected the first cell, and check the properties for text colour, it's set to: ByLayer. Even though the layer has a white colour, the text isn't displayed. If I change the layer, it also doesn't affect the text colour. It remains invisible.
In order to facilitate your help, I'll share the DWG file with only that table in it. See if you can figure out what is happening, please.
You can download it from the link: https://file.io/xS3zflf2iFUQ
Thanks