Serial number ground away? Good.
If you're buying a gun in an illegal handshake deal, why would you want one with a ground off serial number? It's not traceable to you even with the serial number, and getting caught with a gun with a ground off serial number is a federal offence in and of itself. It seems to me a criminal wouldn't want the serial number ground off unless it had previously been legally purchased by them through a traceable deal and they're also planning to dump the gun.
No. You have it backward. Science is not, in fact, about collecting evidence which supports your hypothesis. Science is about collecting evidence which shows your hypothesis to be false. If, after you have tried as hard as you can to disprove your own idea, you still cannot show it to be false, you then ask others to find your error. If they too cannot show it to be false, then, finally, you have something that tentatively might be true.
Anyway, we are not at an early stage in the Earhart crash. There has already been plenty of evidence collected, such as the fact that this island is far enough away from Howland Island (their destination), that they would have had to have been aiming for this alternate island from the moment they took off in order to have enough fuel to reach it. It simply isn't a possible 'we ran out of fuel and have to ditch' location. So the only other possible reason they would hit this island would have been navigation error. But, again, this alternate island is quite far away from the original island. Noonan, the navigator (one of the best of his day), would have had to have made an incredibly huge navigation error. It's just not likely. Possible? Sure, anything is possible. But finding some junk and a skeleton on an island which is known to have been commonly populated is not even close to compelling evidence to suggest that Earhart and her navigator made this particular massive error.
I have a theory that it's impossible to prove anything, but I can't prove it.