If she's no longer obese and just in the overweight range, I would say losing 16 pounds in a month is not even remotely realistic for a female, so I would be inclined to agree with her.
She's already been dieting so it's not like she'll get a big flush of water and glycogen in the next month. Her maintenance levels at this point are probably 1300-1700 calories a day (unless she is a giant). At 16 pounds, we're talking about a calorie deficit of around 1800 calories per day. From diet alone she will only be in a 100-500 deficit.. so in order to drop 16 pounds of fat we're looking at 2-4 hours of cardio a day, 7 days a week.
Guys with weight training experience can drop weight much faster because their maintenance levels are typically 1.5-2x higher than women (depending on how much muscle they are carrying). It's not a question of effort but simply of testosterone and lean body mass.