I believe that these claims are not really lying so much as misleading.
And I mean very, very misleading.
I think what they might be doing is saying that a cartridge has as many milligrams (mg) of nicotine as a pack of cigarettes. So therefore if you ignore the possible fact that we absorb far less nicotine from using electronic cigarettes as compared to cigarettes, you can potentially say that a cartridge could equal a pack of cigarettes. Of course, that is only if you consider that you would have to be taking only like two drags off your electronic cigarette and pretending that you have just smoked a cigarette.
So yeah, if you only take around two drags every time you would normally have a cigarette, it may last as long as a pack. And if you absorbed about the same amount of nicotine from an electronic cigarette as you do from a real cigarette... well, then there you go!!