In John Craven's book, "The Silent War," he talks additionally about the Glomar Explorer and K-129. However, unlike most other accounts, his account has much more chilling implications.
Firstly, a little about nuclear deterance. We are all familiar with the concept of mutually assured destruction. But, one of the caveats of MAD is absolute assurance that your nuclear arsenal is absolutely under your control. Should either side loose confidence that the other's leadership is firmly behind the nuclear trigger, MAD falls apart. It is possible that a rogue will launch a nuclear strike. Or worse, in the event that you adversary strikes, you find yourself unable to respond.
Nuclear warheads contain high explosives to start the nuclear chain reaction. The complex control systems in the nuclear warhead are tamper resistant. I pose this question to you: If you were designing the tamper control system in a nuclear warhead, what would you do if you detected tampering? The answer is to activate the high explosives. You take care of two problems at once. Firstly, you destroy the weapon, making a second (perhaps more successful) attempt impossible. Secondly, you probably kill the person trying to tamper with it in the first place. Of course, you probably also spew radioactive material all over the place. In the sea, it simply sinks.
It is with this in mind that we look at K-129. The Soviets looked frantically for K-129 at 45 degrees latitude, suggesting that its patrol was roughly 750 to 1000 miles northwest of Hawaii. One concludes that K-129's patrol was to be within launch range of Hawaii. However, the sound signatures done by the US Navy concluded that the submarine lay at 40 degrees latitude. This is a big difference. This is not on the path to or from patrol. This is too large a difference to reasonably be made in error. This boat was not where it was supposed to be.
The boat also made no implosion on its way down. This suggests that the boat was on the surface with the hatches open. Why would it be on the surface with all the hatches open? Abandoning ship. There are two main reasons to abandon ship: flooding and fire. If it were operating normally, it would be at snorkel depth or below (it's a diesel). If it were either abandoning ship or launching its missiles it would be surfaced. If it started flooding so severely as to not send out a distress signal, it would probably have never made it to the surface. Likewise for fire. That leaves one conclusion: the captain was trying to launch his missiles when either flooding or fire took the boat and everybody abandoned ship.
It is with this conclusion that it became a matter larger than the Navy. This was a matter for the President. The Navy could have probably conducted the same work that the CIA did, except under water and able to escape detection. However, that was never the idea. The Glomar Explorer was somewhat overt. The strategic value of the classified material was not worth the expense. The "message" was: We know that you don't fully control your military. It was not out of remembrance of the sailors that it was videotaped. It was in case they needed reminding that we knew.
Additionally note, that if a military ship is outside territorial waters, that the first salvager to tie a line has rights to salvage.