Look upthread at what I posted from R' Reuven Feinstein. He doesn't say you need to clarify that the hechsher is up to your standard, he says if 1 eid tells you it's kosher he has ne'emanus. You can also look at the sources referenced in the footnotes, I didn't look at them today, but IIRC they should answer your question.
Are you talking about this?
See below from R' Reuven Feinstein.
If so, unless the footnotes (which I did not check) do, it does not address what I was talking about.
Here's a different question in a similar vein. There is a product sold in many kosher stores with a generally accepted hechsher. I've heard from multiple sources from different hechsherim that while they do usually trust this hechsher, this product is problematic for various reasons. This product is on tables of people I trust without needing a teshuvah from R' Moshe - not the kind of people I referenced in my previous posts. They know halacha, they may even keep stricter standards than I do, but are unaware of the issues with this specific product. Do I tell them what I've heard about the product if I think they would want to be aware? Or do I let them remain an anus because tainting their neemanus in that hechsher will ruin ahavas yisroel?
I see and understand the idea that would she be trusting of each other. I don't see (in your post) that that would apply in instances we have information that neemanus is based on ignorance of halacha or metzius.