There's more legal recourse for a mistake from law enforcement, and furthermore, they aren't going to show cases where you were acquitted. In my case, the background check company reported a crime that I HAD been arrested for but found not guilty of. Background check companies don't do their due diligence in making sure that the records they gather are still valid. I wanted very much to sue the company that cost me that job opportunity, but they've covered their bases enough to shift accountability to the customer.
Basically, they put an asterisk next to their reports saying to take them with a grain of salt. But that doesn't change the damage done by a potential employer getting a peak into your past that they never should have gotten.
Let's say you are mistaken for a wanted robber and arrested and later acquitted or have the charges dropped, when that record is expunged, there is a legal duty for the government to destroy all records related to that arrest.
If they don't, you have political and legal recourse. A third-party company doesn't have the same legal obligation, nor does the public have any democratic control over that organization. Data companies have institutional pressures to preserve data at all costs, not to be proactive in destroying records of innocent folks.
And at least in my state, if you are booked after your arrest, you now have a "prisoner file number" (PFN), even if they release you immediately. This is what a cop is using when they ask if you've ever been arrested before, checking to see if you lie.
"In Europe" is not really accurate here. In some countries it is actually illegal to do any background check at all apart from the ones provided by the state (you can still check if a diploma is real of course).
In some other there will be no real obligation of keeping the records accurate (sometimes there is one theoretical but not enforced, sometimes there is one but with a legal leeway that allows a certain amount of inaccuracy).
In my (limited) experience, mistakes among LEAs is more along the lines of they have data that doesn't match a real person. I'm not saying it doesn't happen, but getting people mixed up isn't something that I've seen.
There's a lot of entropy in first/middle/last names, DOBs, SSN, driver's license, etc. so accidental typo matches just means bad data, not some other person.
Basically, they put an asterisk next to their reports saying to take them with a grain of salt. But that doesn't change the damage done by a potential employer getting a peak into your past that they never should have gotten.
Edit: fixed some typos