For standard letter-size paper in a basic printer, the user can select to Print Actual Size (No Scale) or Fit to Page options. I estimate that a graphic 8" by 10.1875" gets close to not appearing different sizes, but its not exact. What are the dimensions needed so the printed graphic appear exactly the same no matter which scale option is selected?
There is no way to answer this because each printer has a different "live" area for a page. My desktop printer might leave a 10mm border around the edge of a paper, but yours might only leave a 5mm border. That's why "fit to page" is a setting that is controlled by each individual printer driver, because it is dependent upon the capabilities of the individual printer.
There is no such option for most printers, and most printing mechanisms out there. Just simply not going to happen.
However, that said it IS possible to do if you are sending unaltered postscript or eps to your printer as part of the stream and the printer supports postscript. While admittedly this is a far fetched corner case, not likely to work on most printers, it can work. I have once tried to do this as a exercise with some mixed results.
Its just easier to instruct the operator to do it correctly. One nifty way to make the mistake visible is to add internal crop marks. Since most printers can not do edge to edge printing, if the marks are visible then there was a mistake.