I'm more concerned about the effect this has on peoples' perception of our foreign policy. If people understood exactly how easy it is to build a Uranium atomic bomb (I understand we're talking about hydrogen here), they might feel very differently about being ok with Iran saying no to UN or IAEA regulator snooping.
Hydrogen bomb knowledge is still not exactly common (like the uranium bomb knowledge is) so I can understand and even support their interest here. This isn't even about domestic consumption, anybody here could figure it out how to find the info if they really wanted, it's about foreign power