I've had my own background checks in the past and no one has shared them with me. Speaking to HR, unless there is a negative item on your record they aren't required to.
In EU even something like recruiter scribbling notes over your printed CV during job interview automatically grants you right to look into them as it is considered personal data processing.
At least at the federal level, no they don't. Unless they decided not to hire you (or fired you afterwards). Then they only have to provide "a notice that includes a copy of the consumer report you relied on to make your decision" - https://www.eeoc.gov/eeoc/publications/background_checks_emp...
I've requested it, just for my own amusement. They told me no. Unless they didn't hire me based on something from that background check they didn't have to give it to you.
