What is meant by the phrase "which is to say"?

Question

When someone says

... X which is to say Y ...

is there an implication that X is mistaken or false? In this construction is Y generally the opposite of X?

Some random examples from the NY Times:

"When you are unemployed, which is to say when you are underfed, harassed, bored and miserable" (source)

"But corruption levels are around the global average, which is to say, corruption is rife" (source)

"There are journalists who cover the world of ideas, which is to say they report on the lives and work of people who have them" (source)

Answer 1

In earnest writing, the phrase can be used so that Y clarifies X.

However, it is a typical witticism (as in your examples) where Y is a cynical statement about X, almost treating X as a setup premise for the humor in Y.

Answer 2

It can mean that X is a euphemism (or similar) for Y. They don't necessarily have to be opposites.

Edit: and indeed, looking at all of your examples, I'd say they fit that pattern. "Unemployed," for example, sounds (as bad as it is) much better than "underfed, harassed, bored and miserable."