Wrong, ex. Think about it. Take a set of, say nine numbers (I'll even skew them):
14
17
18
19
22
29
37
55
79
The median is the 5th number, 22. Then, subtract 3.1 from all numbers:
10.9
13.9
14.9
15.9
18.9
25.9
33.9
51.9
75.9
The median is still the 5th number, 18.9. The difference between 22 and 18.9 is, of course, 3.1. The mean will always be more than the median in a right-skewed set, yes, but that doesn't apply here since no one is talking about the mean and we're just shifting the whole data set.