I failed a background check once because they even ignore middle name/initial. The record in the system had a different MI and I provided mine. Also, birthdate, location, race, etc., were all mismatched. Thankfully, in that case, I was able to provide documentation that I was not a match, but it is incredibly frustrating to have false positives and no "this is positive but it is obviously a partially incorrect match. In the OP's hypothetical about a pre-screening background check, you might never get the opportunity to clear your name.

And most systems and forms in the USA only provide for one middle initial, which makes things tricky for those coming from other cultures.

They do unfortunately. I know someone with a more unusual surname who was getting chased for the debt of someone with the same name. It happens.