「～～というのだ」、「～～というの」、「～～というのか」, etc. added at the end of a question generally functions to emphasize the question itself.
By adding one of those phrases, you are expressing the fact that you really want to know the answer because whatever happened that caused you to ask the question perplexes, surprises, shocks you, etc.
Thus, you will not attach one of those phrases just to ask someone what he had for lunch or where he got his new haircut. You probably will attach one, however, if you see a friend coming out of a restaurant looking very sick or bump into him with the weirdest haircut.
Does the usage of という have any relevance to the way the information has been obtained before they ask the question or is it purely for emphasis or some other usage?
I find this to be a very insightful question. In real life, the way the information has been obtained would generally have very little to do with the use of 「という」. It is the content of the event/situation that matters such as how puzzling it is.
In this particular case, however, it is fiction where those questions are uttered. "Birthmarks shining" is a highly peculiar event: therefore, one could say that the way the information has been obtained would have much to do with the use of 「という」 here.