I won't comment on the driving aspects of the video.
Some simple facts about copyright:
1. A copyright registration is a prerequisite to suing for infringement, i.e. if you don't have the registration, you can't get in court (there are limited exceptions involving foreign works but they're not pertinent here).
2. Post-registration infringement entitles you to statutory damages, i.e. you can only get actual damages for infringement before you register the copyright. Statutory damages are, usually, much higher and don't require proof of harm.
3. A copyright registration creates a legal presumption with respect to validity, ownership and date of creation. This means that, if you have a copyright registration, the accused infringer has the burden of proving that the copyright isn't valid, you are not the owner of the protected work, and/or it was not created prior to the accused infringer's copy.
4. Independent creation is a complete defense to copyright infringement. Good luck trying to prove it, however.
5. Copyright protection begins the moment the work is fixed in a tangible medium. For music, this means written down, recorded to tape, saved as digital media or, in some circumstances, broadcast live.
6. Copyright infringement is strict liability. This means that someone is liable for infringement even if they lacked any intent to infringe or even knew they were infringing.
The video mentioned trademark. Trademark is an entirely different species of intellectual property protection, serves an entirely different purpose and has entirely different requirements. It's too involved to go into in this post but, unlike copyright, requires more than simply registering the mark for protection to accrue.
PTravel, Esq.
I'm a real IP lawyer, I don't just play one on the internet.
Edited to add:
One more thing. The video mentions "poor man's copyright," and Greg is right in that it's not particularly helpful, but not for the reasons that he mentioned. Self-mailing is relevant evidence of date of creation and all relevant evidence is admissible in a copyright infringement action. The trier-of-fact, who may be the judge or may be a jury, must decide how much weight to give to the evidence and, as Greg mentioned, the fact that a self-mailing can be easily faked definitely weakens its probative value -- just mail yourself a bunch of unsealed envelopes tomorrow and, in the future, drop recordings into them as you write them. However, as mentioned above, you must have a registration before you can sue for infringement, the registration entitles you to an alternate measure of damages that can be considerably higher, and having a registration shifts the burden of proof on key issues to the defendant who is accused of infringing.