They claim [it is true, since]the process of digesting the "tough to digest" fiber present in celery takes more calories than the 8 calories per stalk of celery.
-- Nicole (last name withheld) Alberta, Canada
Although cellulose (the "tough to digest" fiber the show refers to) can not be broken down by humans, it does not make celery a "calorie-negative" food.
The Mayo Clinic specifically looked into this nine years ago and concluded that celery does not result in negative calorie deficit.
Simply put, its thermic effect (the amount of energy it takes for the body to digest it) does not surpass its caloric content, especially given that its thermic effect burns approximately 0.5 calories.
Even if celery was discovered to be a negative calorie food, it wouldn't be a life-changing discovery.
If each stalk resulted in a two calorie deficit, that would mean it would take 25 stalks of it (plain -- no dips allowed!) to simply burn an additional 50 calories.
Or, you could quickly slash 50 calories from your day by replacing your standard Starbucks Venti beverage with a Grande, or starting off your morning with a medium orange rather than a cup of orange juice.