Neither the article nor the title actually talk about inflating numbers, which is how I read it at first too. They only talk about actually increasing the number of users, by sending out invites: "Another example of the lengths LinkedIn will go to in order to increase its user base."
But it's far more likely that it's just an error of judgement, involving no formal or informal logic at all.
Namely, nobody, including OP, made the syllogism you present, with the neat "therefore, X must include" etc step.
They simply thought that it's very probable that this is what LinkedIn did to inflate their numbers.