Skepticism based purely on the laws of probability, actually, which is the basis for the entire scientific method.

Scientist are a very skeptical lot (I say as one myself), because there are a lot of random flukes out there. If you want people to take your work seriously, you're going to need
at least a 3-sigma detection in the hard sciences, often much higher (i.e., showing that the chance of what you observed happening
purely by random chance is so small that it makes more sense to believe it happened as a result of something deterministic, usually a hypothesis you're positing support for).
But hey, if you want specific points addressed, I can do that too.
The photo, at this point in the thread, seems to have been pretty conclusively dated to two years before Earhart's disappearance, so I won't discuss it specifically, instead focusing on other points (I remain open to new evidence in this area, of course!).
That video…hoo boy. I watched it, and if I were to write a scientific paper with that slapdash level of quality it would be laughed out of every scientific journal on the planet. Leaving aside stuff about the photo (although I could go into that quite a bit too, such as false-positive rates for facial recognition and how seemingly only a single person did the analysis):
- There's a file missing from the Office of Naval Investigation. Ok. Great. Is this an isolated instance? We're only told of one, which makes it sound like some big conspiracy or cover-up, but it could also have just as easily simply been misplaced. The ONI isn't infallible. How many other such files are missing? I'm sure the ONI loses, misfiles, or accidentally throws out things like other organizations do, and the farther back in time we look the more likely it is. We're never told how many other files are similarly missing, so we can't make a quantitative judgement of the rarity of this situation.
- Even if it's a very rare thing to happen, it could still be down to simple human error. No government cover-up needed.
- For that matter, the video takes this missing document as somehow evidence for its theory. We don't know what was in it. Maybe it was a boring technical report on the economic conditions of the Marshall Islands. No one knows, so taking it as evidence of a government cover-up is a serious leap of faith. That's the beauty of a conspiracy theory, that it can take the very lack of evidence for something as evidence for that something having occurred.
- Ah, yes, this anonymous Marine Corps commandant. No name? Not even a picture of the letter he supposedly wrote? Seriously, this is basic level journalism. There's no way to check or corroborate this story. All we have is the presenter's word to go on. (Note that I'm not seriously suggesting the presenter is deliberately lying in this case, but would it kill him to at least mention a name??)
- Being on the internet as long as I have, the phrase "We all know X" is an immediate red flag to me that X is probably not true and the speaker is trying to drum up support for their position by making it seem as if disagreement would be going against common knowledge. Anyone can claim that "We all know X" without it being true. ("We all know Paradox actually had the content for TfV and DoD ready to go at launch and chose to cut it for DLC later!")
- For instance, we don't know the context of this mysterious letter. Was it a simple, matter-of-fact letter to a fellow commandant acknowledging something that was, indeed, common knowledge to both of them? Or was it a paranoid conspiracy theory to a fellow conspiracy nut saying "C'mon man, we all know that she was killed in Saipan, and that Martians have been stealing our cattle for decades!" The context is important in assessing credibility of the source.
- And let's say it really was common knowledge among at least some people in the military. Are we seriously to believe that not a single person in possession of this secret (beyond this one anonymous guy) ever spilled it? No one, on their death bed, in fear of no government reprisal, ever went "Yeah, actually the government's been covering it up all along, but I know what happened to Amelia Earhart."? No one wrote a sensational exposé in search of fame and riches? No one ever accidentally let it slip while drunk? The more people know a secret the harder it is to keep it. Believing this requires a far greater faith in the ability of the common man's secret-keeping capacity than I have.
- [mini rant]The guy in the video says at 3:52 "We have no evidence anywhere that she crashed into the ocean […] I think we have a lot of evidence that she lived and survived in the Marshall Islands." Well, of course we wouldn't find evidence if she crashed into the ocean! We would expect to find no evidence! The Pacific Ocean is huge. I live in Hawaii, surrounded by it, and have a faint inkling of just how enormous it is. A single plane and two people going missing somewhere in the Pacific Ocean and no evidence ever being found is overwhelmingly the most likely possibility (see also, that Malaysian Airlines flight where we—finally, after a year—got incredibly lucky and found a single bit of debris). Absence of evidence is not evidence of absence. Not finding evidence that she crashed into the ocean is entirely in line with what we would expect if she did, not evidence that she didn't crash into the ocean! [/mini rant] This twisting of logic to sell a story is seriously frustrating to me as a scientist.

Ok, I think that addresses all the non-photo-related points, but let me know if I missed one and I'll be happy to address it.