By outsourcing he merely means delegating work to someone who is not an employee of the company - or rather, "to a freelance designer or firm." The OP makes no distiction between or contention for or against local, domestic or international workforces.

Outsourcing is done for efficiency from a startup sense. Is it cost-cutting? Yes, because to begin with you are probably running tight margins and an expensive contractor can be done at the end of his contract, but an expensive in house designer (who might not be a developer) is benched after the work is completed. The cost of acquiring an inhouse designer solely for UX/UI does not make sense when you need all hands to develop your functional features. (In the case of a startup - this probably does not apply as much to Skype)

Comparing ANYSITE.com to facebook.com can be generally assumed to be hand-waving given the degree to which facebook stands as a massive outlier to any set of startups regardless of how similar the ideas may be.

It doesn't seem like you read the article.

The author doesn't suggest offshoring at all, just whether or not he can use an outside agency for design or UX.

In the short term, outsourcing in this sense is generally more expensive than handling it in-house, though in the long term, obviously the costs of maintaining a dedicated employee can tip the scales on the overall cost.