Hi there, thanks for your thoughts.
I sort of agree with you in a limited sense, and in fact thought about mentioning the lack of a (Constitutionally based) press privilege. However, I think in our hypothetical there are a couple of things going on that make it more complicated.
1) There is (at least potentially) an actual destruction of evidence, as opposed to simply refusing to divulge a name.
2) The person who is refusing to divulge information/destroying evidence is the head of the organization which is at the root of the alleged criminal conspiracy.
Obviously, I spend all day splitting hairs, but this second one makes things a lot more complicated in my opinion. You have an organization concealing information about the organization itself. The press is usually attempting to conceal sources which revealed information about unrelated third parties that was revealed because it was thought to be in the public interest.
Our hypothetical seems closer to a situation in which several staff of a major newspaper were charged with crimes, and the editor in chief refused to reveal where he obtained information about the reporters criminal activity.
Finally, you mention the Spousal Privilege and 5th Amendment right against self-incrimination. Those are both specific immunities provided for under the evidence code. In general, these privileges provide that certain persons may not be compelled to provide evidence against someone (this area is a bit too complicated to discuss at length here). In our hypothetical, there is no valid evidence code exception. The closest thing I can think of is that some states provide a "social worker exception", but I think that argument would be a bridge too far under the instant facts.
At the end of the day, there is no Constitutionally guaranteed immunity to the press, and there certainly is no immunity to private citizens (that would apply in our hypothetical) which would allow a person to ignore a court order. The reason for this is because a person's innocence or guilt is too important to be influenced by private actors because of moral/professional/personal considerations. Just some guy does not get to choose what he does or does not reveal to the court, particularly if a person's life is on the life. It doesn't take a lot of imagination to see how that would lead to an unworkable system. Happy to has this out a bit more if it doesn't make sense.