This is bad advice citing comically-bad examples of the practice to criticize the practice. Yes, the specific examples given there are all bad and unnecessary, don't do that.
But that's not what bracketed editorial interpolation is for, and editorial interpolation isn't, as the article (paraphrasing the AP manual) pretends, an alternative to paraphrasing, it's a mechanism of paraphrasing which makes explicit what is paraphrased and what is preserved exactly. Used well, it preserves the important parts of quote while maintain flow around paraphrases necessary to preserve meaning from context in the source that was omitted. E.g., replacing a pronoun with it's referent/antecedent when including the portion of the text that provides it in a way which preserved the relationship would require a much longer quote with more material extraneous to the purpose for which it is being quoted.
The comments about trust are kind of dumb. If I use quotes with no editorial interpolation, I ask just as much trust as I do with editorial interpolation: I could, after all, just be inventing thee quote whole cloth, or presenting it accurately but misleadingly out of its original context. The only way to be sure that I haven't misrepresented the origin, text, or sense of the quote—whether or not I have marked interpolations in it—is to check the source, both to find the quote and understand it's context.
As are the bits about exact text search: it is extremely rare that editorial interpolation will fail to leave enough unique uninterrupted text to allow an exact text search to take you to the right part of the source material if the original source is exposed to online full-text search in the first place.