I'd say they're probably taking Polybius at face value where he says in 2.24 that "the grand total of the forces actually defending Rome was over 150,000 foot, 6000 cavalry: and of the men able to bear arms, Romans and allies, over 700,000 foot and 70,000 horse". If there is a specific claim that Carthage also had 700,000, I'd be very skeptical. I don't know of any census performed the Carthaginian government. If I remember correctly, the city of Carthage is estimated to have had a population of around 50,000; Phoenician colonies were usually very small and loosely-knit.

As hard as it may be to believe, Rome did field large armies. They fielded nearly 80,000 men at Cannae.

This paper goes into some depth about the population of Rome and how Polybius and others may have arrived at their figures. It also compares a lot of other estimates for Rome and Italy's populations.