You may create a field with a table calculation:
Make it a Discrete (Blue Pill),
Compute Using Table (Down),
Place it to Rows at the leftmost position,
set Show header to Off (clear a flag).
Hope this helps.
First of all I suggest you push back on your users (if you haven't already). Why do they want a text table? What do they want to do with the data from the text table? What are they going to do after that? For example if the users are looking for a crosstab that they can export then what are they going to do next with that crosstab? If they are looking to analyze data in some other tool then is that analysis something you can set up in Tableau?
There are likely answers there that can lead to finding alternative visualizations that are a) help the users more than a text table and b) are easier to construct in Tableau. Part of why I suggest this is the text tables are horrible visualizations, they are only better choices some of the time when we are wanting to look up exact values.
Here's an alternative solution to Yuriy's: Duplicate the dimension fields being used on the Rows Shelf, put those duplicates on the Rows Shelf, and turn off the headers:
Personally I'll use this more than an INDEX() calculation to get the replicated results because it avoids unwanted densification (where table calculations are triggering Tableau to pad out the marks in the view).