My understanding is that we have been able to take direct radio interferometery distance measurements of Mars since the Viking and other landers were there.
That sounds right. But, to get the numbers in the www page, you can't just measure where it is. You have to about predict where it will be, which requires forward integration of a motion model for all the mass in the solar system. The paper I referenced cites Mars range measurements, and related measurements, as a check on this forward integration.
Planetary radar is another option for a ground truth check even if you don't have a radio source (like Viking) on or near the planet in question.
