In the context of determining an objective truth value, they are not wrong.
In the context of determining and objective truth-value?
First, please stop talking about truth-values; they're not what you think. Second, how does one 'determine an objective truth value'? I suspect you mean to say 'in the context of confirming whether a proposition is true (or false) by observation'.
It is true that being unfalsifiable does not determine truth or validity
What does validity have to do with anything? I think you're just throwing around clever-sounding words.
and she even says that claiming to know that God is unfalsifiable is a knowledge claim.
Right, claiming to know something is a knowledge claim ... duh? I think you meant to say something else, right?
However, they are not talking about unfalsifiable in the sense of "This cake is delicious." or even "I saw some guy cross the street." They are talking to a man who admits that he essentially does not know but believes anyway because it can't be proven wrong and it makes him happy.
Which is different from most atheists, how exactly? Need anyone be reminded that atheism is not
scientifically falsifiable. Yes, there are logically possible observations that would falsify atheism, but this is a
very weak kind of falsifiability. Why? Because atheism doesn't make any
precise predictions that we can test. For example, it predicts that God will never descend from heaven and bring judgement upon non-believers, but the prediction is unbounded: the experiment, so to speak, can never be completed. Perhaps this falsifiability is better than nothing, but it's not much to brag about either. In any case, atheists typically make all kinds of metaphysical assumptions, such as materialism, reductionism, empiricism, realism, and so on, that all exemplify unfalsifiable theories about the fundamental nature of the universe.
In his context it
can't be given a truth value. At least not in that point in time. That is not to say that no unfalsifiable thing can be given a truth value.
If we wait for "knowledge" before giving something a 'truth value', then we'll never get anywhere. The caller on the show might have been hopelessly confused, willfully irrational, and probably quite stupid, but the hosts just responded with their own bad arguments and atheists shibboleths. Heck, I'm an atheist. I've always been an atheist. However, atheists like this are more likely to convert me to Christianity than any theist I know.