I doubt they really care whether the translation is accurate, or rather, that they bother to give any consideration to whether its accurate or not. I feel like most of the time there is a lot of confirmation bias involved.
Rather than looking to see what something says, they look for something that agrees with the point they bear some favor of.
I don't know about confirmation bias on the part of the reader, but "translations" are subject to interpretation especially when you're dealing with a really ancient version of a language. I know the KJV old testament itself has been "re-interpreted" at least once since the version I read (and questioned) as a child. Very few people can read or have access to the original "texts" and are dependent on "experts" for translation (each "expert" having their own confirmation bias, maybe, to slant the story or decide whether it belongs in the canon). Also, people aren't really known for thinking for themselves much.
Translation of documents from one language to another is very tricky. Anybody that speaks two or more languages is aware of this. When I was coordinator of the first chiropractic school in Brasil in 1998 I became very aware of this. The intent of words from one language very often does not translate correctly. This work must be left to the work of scholars in the appropriate field. Now imagine the complexity and importance in a sacred document .
Glad you raised this question again Rabbi. You make a very relevant point. Watered down versions can be a great blessing or a hindrance depending on who you speak to. Unfortunately our generation wants to get spoon fed without chewing the material.
God Bless