I am not your lawyer. The useful distinction is technical and it is also the one the argument hangs on. A patch file stores the difference between two files. A ROM dump stores the game. Distributing a dump of a copyrighted game is the act people get in trouble for. Distributing a patch still depends on what the patch contains and on the rights of the people who made the game and the hack. Wikipedia's ROM hacking article is a definition of the hobby, not a ruling. 17 U.S.C. §512 is the notice-and-takedown procedure, which is why the DMCA page exists. It is not a finding that any particular patch is lawful.
This site does not host ROMs and does not host patch files. Guides link to author pages when I have checked a page. If a link is absent, I did not have a page I was willing to call the author's. You apply a file you obtained yourself. If a rightsholder wants something removed, the DMCA page says what a notice should contain and where to send it.
Emulators and patches get discussed together and they are different programs. An emulator is a piece of software that runs a file. A patch modifies a file. Neither fact, by itself, tells you whether your copy of the game is licensed. I will not add a paragraph that says homebrew is always fine or that every hack is fair use. Those are conclusions I am not drawing.
Related pages: the DMCA contact, the safety page, and the how-to page for the technical steps. If you need a legal answer about a specific game, ask a lawyer in your country. The statute I linked is United States code.
