The real problem is they are looking at written data. Sarcasm is based on auditory and visual cues of the person. Detecting sarcasm online is like looking for a needle in a haystack when you don't know what a needle or hay is.
To some degree yes, but there are still satirical works of literature throughout history such as Swift's A Modest Proposal that would pose a similar problem. The problem in understanding sarcasm or satire without the visual or vocal cues relates to understanding meaning (a difficult problem in its own right) as well as why a particular response is absurd given the context, which means you also have to know what the expected or typical answer should look like.
Both of you are right... and wrong. The problem is that most people don't know how to write - and thus what they mean as (what they misunderstand to be) sarcasm doesn't come across as such. That's the real problem the researchers are facing, lack of ability to convey meaning, not lack of context.