It's not that hard for a terrorist group to sneak in shoulder-fired STA missile.
True, but as Woolfe points out there is great risk in covering up something like this. There is also great difficulty in covering up something like this. We know in the past that the government has covered up evidence of acts of war, no doubt to avoid being pressured into war, but it's difficult to imagine why any nation with which we would fear a war would bring down this particular aircraft. I suppose it's possible that the government would want to cover up a terrorist act such as this, but I can't imagine why, nor can I recall any other such incidents. Cover up foreknowledge, yes, but not covering up the actual terrorist act which is much more difficult and without (at least to me) such self-serving reasons for the cover-up. Without a compelling reason or historical precedent, I have a hard time believing that this happened.
As far as a shoulder-fired missile, I don't think this really fits. Most shoulder-fired missiles are IR homing, so the missile should have taken out an engine rather than going for the center of mass which requires either a very sophisticated guidance system or continuous control. Neither is beyond the realm of possibility, but neither seems particularly likely for a singular terrorist event. Also, most AA missiles are proximity-fused; this seems to be something large enough to almost immediately destroy the structural integrity of a very large and relatively robust air frame. Today such missiles are not at all uncommon due to the anti-missile role, especially launched from ships, but I don't think they were that common in 1996. That's why I lean toward either a strike from a wayward training missile with an inert warhead, or an inadvertent launch of a large ship-borne AA missile.
It's possible that this was an early test of a missile defense missile, but three things argue against it. First, such missiles are generally widely hyped by the manufacturers. Second, the military exercises in the area seem to have been fairly routine - not the kind of situation (especially given the proximity to busy flight paths) for such a test. And third, missiles in early tests often go haywire, so they are not generally tested in any kind of military exercises until very mature and type-classified. One thing is for sure: For something like this to happen as an accident, several things have to fail or break at the same time. We have some pretty good evidence that one such thing did happen - the naval group was too close to the shipping lanes - but the official story is that this dd not happen. When we have sufficient evidence to doubt the official story, but not sufficient evidence to disprove the official story, how can we really know what happened? That's why I likened it to JFK's assassination. Both have things that really cast doubt on the official story without enough evidence to establish what did happen, or even that the official story is actually wrong.
Very early on the NTSB seemed (to my untrained observation anyway) to go into cover-up mode. For instance, seizing rather than copying radar tapes, including back-ups, and seizing film media (including threatening jail time for copies) but not cameras. In evaluating film it's often very useful to have the actual camera, but it's hardly useful to have copies of the film or digital media. That suggests to me that they knew from very early on the need to cover up the incident, because it normally takes time to figure out what happened. If a terrorist fired a shoulder-launched or even launcher-launched missile, surely it would have taken some time to figure out what happened, present this information in preliminary form to Clinton, have him decide to cover it up, and then implement the cover up. And everyone familiar with the investigation up to that point is a security risk. I don't think it's possible to have a cover up of something of this magnitude without almost immediately making that decision, else someone will surely disagree, or have an attack of conscience, or simply hate Clinton too much to keep the secret.
It's also possible that there is something behind the scenes that led to this looking like a cover up without that actually being the case. Sometimes coincidences do happen, and even Freud knew that sometimes a cigar is just a cigar.
EDIT: Also, apologies to Flexy but I still haven't watched the video. Was going to listen to it, but the password did not work for me.