Just taking a few other data points, Twitter (when it was Twitter), had around 7k people, and strikes me as a similar sort of product to LinkedIn, at least the same ballpark. Google has somewhere around 180k (according to public info), and has many products that feel like a LinkedIn sort of size.
Whatever you may think of my other examples, LinkedIn really does seem like an outlier? Am I missing a major aspect of their business? It's a social network, a recruitment service, an ads business. Is that 22k people?