Nah, there is obviously a reason why you deleted the messages I made a comment to....
There exists a lot of fake trees out there, and when people claim undocumented connections to royals we always ask for all details, - both to give people a chance to prove it, but also to help searching for sources that tells something else. That is not being bitchy, but to help you.
Geni's goal is however having a would tree and I can guarantee that your version of Christian IV would be merged into the world tree, so we should check your "son" before it happens.
Many such connections was made by genealogists, even professionals taking money to find such a connection in the growth of nationalism before WW2. At that time we could not check primary sources as today. Those connections has lived on as "family secrets" but also when printed in a book - it had to be true?
Some years ago a Norwegian family claimed hardly such a connection and even went public about it and even worse changed their last name to be more "royal".
Among Norwegian royalists there was a large discussion about it and all arguments was pulled to pieces, but it was claimed that there had to be falsification of the church records to "save" this king. Finally the family agreed on a DNA test, which finally closed all speculations on such a royal connection.