I left out an important piece of information. My users will need to input and modify text, which doesn't seem possible.
The help is a little misleading because it says:
Values of an input field can be changed in list box cells, table box cells and in table chart expression cells.
Text is not addressed or excluded specifically.
No, I don't think you can modify string inputfields in a table chart.
You could use a table box or list box, though.
And here I found a similar request and a possible workaround.