The law can be confusing at times, and then people go to court to figure out what the law actually means. I think consulting proper interpretation of the statute is the first step to knowing what law is in your jurisdiction, as different federal circuits sometimes have differing interpretation of the same law.
That being said, when somebody says... "is this a crime?" Means in legal terms that the act that you do falls within elements of a particular offense. An element is something that 12 jurors need to agree on that it did in fact happen.
As such... you cannot steal your own mail from the neighbors mail box, because the mail is yours. But, you maybe able to steal your neighbors Netflix subscription. So recording the incident and showing that you took nothing but your own mail, would go against allegations that you did in fact steal something.
The statute can be divided in three sections
A. Whoever steals, takes, or abstracts, or by fraud or deception obtains, or attempts so to obtain, from or out of any mail, post office, or station thereof, letter box, mail receptacle, or any mail route or other authorized depository for mail matter, or from a letter or mail carrier, any letter, postal card, package, bag, or mail, or abstracts or removes from any such letter, package, bag, or mail, any article or thing contained therein, or secretes, embezzles, or destroys any such letter, postal card, package, bag, or mail, or any article or thing contained therein; or
B. Whoever steals, takes, or abstracts, or by fraud or deception obtains any letter, postal card, package, bag, or mail, or any article or thing contained therein which has been left for collection upon or adjacent to a collection box or other authorized depository of mail matter; or
C. Whoever buys, receives, or conceals, or unlawfully has in his possession, any letter, postal card, package, bag, or mail, or any article or thing contained therein, which has been so stolen, taken, embezzled, or abstracted, as herein described, knowing the same to have been stolen, taken, embezzled, or abstracted—
B. and C. are not pertinent because they do not pertain to getting mail. B talks about getting mail from a drop box. C talks about possessing stolen mail
So section A seems to be a long string of words. Maybe we can break it down and make some sense. Consider this, an element can be composed of different means, on which the jury does not have to agree. (See Mathis v. United States). For example if you attack somebody with the weapon, and the weapon element includes different means, like bat, nun-chuck, pipe etc... the jury would not have to agree on which weapon it was, as long as it is listed in this statute. It all really depends on wording. I strongly suggest you read the above case.
As such:
Whoever
(it appears this element describes different actions of taking)
steals, takes, or abstracts, or by fraud or deception obtains, or attempts so to obtain,
(element describing location)
from or out of any mail, post office, or station thereof, letter box, mail receptacle, or any mail route or other authorized depository for mail matter,
(Clarifying element describing location, including a part of the letter)
or from a letter or mail carrier, any letter, postal card, package, bag, or mail, or
(an conditional element of action describing partial removal/opening)
or abstracts or removes from any such letter, package, bag, or mail, any article or thing contained therein, or secretes, embezzles,
(an conditional element describing destruction)
or destroys any such letter, postal card, package, bag, or mail, or any article or thing contained therein;
Lets remove the conditional elements, since they are not pertinent here, further lets see if we can remove everything that did not fit with your action
So you "took" from "post box" a "package." At first glance that does constitute an offense since it meets all the elements. But... what does the word take mean in the context?
For an insight in Seventh Circuit read UNITED STATES of America, v. Christi Kay Jo O'HARA. 139 F.Supp.2d 998, (N.D. of Indiana May 3, 2001)
I would interpret take to mean taking something that is not mine.
In the end it comes down to proof. If the neighbor saw you take something, how can they prove that you took mail? Did they see that the box had a post office stamp? And where did it come from? An interesting topic for ligation.
To remove yourself from the possibility of criminal litigation either get to know your neighbors, or do it quietly in the dark when nobody can see you. LOL.