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I'm disappointed in the community note. You'd think they'd have learned the thing most high school seniors do/did. Don't quote the Wikipedia article. Instead, quote the reference in the Wikipedia article. Much stronger of an argument.
Wikipedia editor here; there's some nuance. This article is listed as a Good Article, meaning it's been reviewed by another (almost certainly) experienced editor for verifiability, prose and style, coverage, neutrality, stability, etc. This was attained in 2013, and especially for such a prominent article, slipping below those standards is a recipe to get GA status revoked. Presumably this note is summarizing a large portion of coverage by Wikipedia and thus a variety of sources. You want to read and cite all of the sources rather than Wikipedia in something like a research paper, but for just a community note, there's really nothing wrong with this.
I believe there are limited sources that are valid on community notes, including Wikipedia
Also, his family doesn't just believe that the FBI was involved in his death. They provided convincing enough evidence for a judge to rule in court that the US government was responsible for MLK's death.