This is silly. Imagine a world where this would be enforced.There is no way to know in advance that your look and feel doesn't accidentally resemble some of the existing millions of websites.
I agree with you and so does the law.
The first required element of proof in any copyright claim is that the alleged infringer had access to the plaintiff's copyrighted work. Basically if you never saw the copyrighted work you are not infringing if your work is substantially similar or appears to be a derivative work.
For another reason why copyright probably (I say probably because you can never predict how a jury will decide) does not apply is the merger doctrine. That is when an idea and the expression of the idea become one. That is not copyrightable.
For the UI to have a trademark, and it could, the 37S UI would have to cause a person to recognize that the UI is by 37S. This will be very difficult for them to achieve. The Nike swoosh is trademarked because it immediately causes a person to know that it is by Nike. Same with the Reebok symbol. A person knowing who designed a UI on a web app by its colors is a stretch.
Also, functional elements cannot be trademarked. So an excellent screen layout that improves usability cannot be part of a trademark. But the colors and artistic arrangement could be.
Lastly, yes, you do need to register your copyright to sue. No, mailing yourself a copy does not work at all. Do not do it. Read 17 U.S.C §412 for the reason. http://www.law.cornell.edu/uscode/uscode17/usc_sec_17_000005...
Then go read §504 and §505 for more reasons.