Pig has a wide range of figurative uses - They're nearly all "unfavourable", but they're certainly not all "offensive". For example...
A wall where the bricks aren't laid level is said to have a pig in it.
To make a pig's ear of something means to do it badly, wrongly or awkwardly.
Pig-iron is crude iron from a smelting furnace, cast in oblong blocks (ingots, or "pigs").
In the current (Euro-) economic climate, PIGS and PIIGS obviously carry "unfavourable" connotations. Any/all of the "anacronymised" countries could bring down the Euro, with potentially disastrous economic, political, and sociological consequences for millions of people.
Collectively referring to these countries as PIGS (rather than SPIG or GIPS, for example), is just dry humour reflecting the fact that collectively they represent a pig of a problem.
EDIT: Per comments below, it seems "I finished the maths exam, but the last question was a pig" is primarily British usage. This answer already has two downvotes, so I'm guessing some people find all figurative usage of "pig" offensive.
From my (UK) perspective, this usage of PIGS is similar to WASP (White Anglo-Saxon Protestant). It's obviously intended to be derogatory/disparaging, but the word itself isn't offensive.