A lot of people aren’t getting the crux of your question. As you say the checksum and the file often come from the same site, this does nothing for increasing trust. However there are situations where you might retrieve the checksum from a trusted source and the file from elsewhere. If the file is big you could go get it via BitTorrent then download just the checksum from the trusted site to check the file wasn’t tampered with. But yes if you don’t trust the source of the checksum it means little for you.
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