There are basically 2 parts to this:
How Many Calories Are In a Big Mac®?
The number of calories in a Big Mac® varies by country, but the figure given of 540 calories is accurate for a US Big Mac®.
How Many Calories Does Running Burn?
The number of calories burnt per minute when running depends on how much you weigh and how fast you run. The following table (found on Runner's World, data taken from Compendium of Physical Activities, January 1993 issue of Medicine and Science in Sports and Exercise) gives the number of calories burnt per 10 minutes of running.
There's no precise definition for jogging, but it's usually taken to mean running slowly, so I'm going to take numbers from the 12 min/mile column.
The average weight for a woman in the US is 74.7 kg (164.7 lb), so that gives a figure of around 97 calories per 10 minutes of jogging.
Putting these 2 answers together, I'd estimate that it would take around 55 minutes of jogging to burn off the calories in a Big Mac®. This is fairly close to the figure of 1 hour 5 minutes given in the article.
This figure will vary considerably depending on your weight and how fast you run.
Is This Type Of Information Useful?
Providing Calorie Information on Fast-Food Restaurant Menu Boards: Consumer Views
The above study compared different approaches to nutritional labelling of fast food. It found:
When asked to compare a menu that provided calorie information for each menu item with a menu that provided the number of minutes of running that would be required to burn the calories contained in each menu item, 71.0% of participants preferred the calorie information over the physical activity information.
Many of those who preferred calorie information viewed the physical activity information as discouraging, a scare tactic, or not generalizable to everyone.