Learn English – What does this “would” mean

Hard to say without more context.

Apologies that this post will reveal more political opinions than are necessary, but it's difficult to explain the full context without that. I am imagining from the context that you are listening to right-wing talk radio. In America, right-wing talk radio is characterized by quite a bit of use of heavy-handed sarcasm.

Then the dialogue is probably something like this:

Speaker: [reads a quote which he feels is very obviously something erroneous or misguided, expecting the listener to agree] Who said this VERBATIM? [the verbatim emphasizing that the speaker is giving the exact quotation, as though the quotation were so shocking that it might sound like an exaggeration]

(I don't know if this is the speaker answering himself, or a second party answering) Well... Obama?

Speaker: That would be right!

It is a sort of sarcasm. To the speaker, it is so OBVIOUS that Obama would say something so ludicrous that his posed question is trivial. So he sarcastically answers with the hedging conditional tense "that would be right" rather than the "that's right." But it means the exact opposite of a hedge.