It doesn't mean that. If someone moves on to the SVR, they are almost certainly paying a much higher rate than they could pay if they shopped around for the best deal.
As an example of how this might happen, say someone gets a 5 year fixed rate mortgage when rates are relatively high, so their rate is 5%, while prevailing SVR at the lender is 8%. Over the 5 years, rates come down so they could get 2% on a new 5 year fixed deal. But they stay on the same mortgage and move on to the SVR, where the rate is now 5%. Their monthly payments don't change, but they could be paying a lot less by moving to the new fixed rate deal.