Having gone through this with several employers, the largest company doing this verification is HireRight. HireRight is BEYOND incompetent at every single level. They refuse documentation such as offer letters on company letterhead to prove a title. The only documentation they accept from applicants is highly sensitive tax documentation from the IRS, which of course does not contain titles but incidentally reveals compensation details they can hoover up into their database but is not relevant to the purpose they were hired by your future employer to do.
If you think credit reporting agencies in the US are Machiavellian and maliciously incompetent, wait until you deal with employment verification firms, they're worse and often the same corporate entities (as noted in the article, another large one is WorkNumber owned by Equifax). These entities put most of the work onto the candidate, display no competence or care for accuracy whatsoever, and generally deliver intentionally misleading or inaccurate results to your future employer. It's so pervasive, that my own complaints to my recruiter were heeded and understood because in their words "oh their reports are always wrong about employment history, we only pay attention to the criminal background check part."
So, in short, no you can't simply provide a valid offer letter showing the title you were hired with to prove that title or to prove a promotion.
This all occurred after I had accepted the job offer and took a long and stressful time.
Same situation for me, which is especially problematic because it's standard practice for offers or start dates of employment in the US to be contingent on the return of a clear background check within the first 30-90 days. Which means you might have already started onboarding to the new role and still be fighting with HireRight (has happened to me 3 times in ~18 years). More annoyingly, HireRight's own databases don't refer to previous points in time when you've corrected their errors, so each time starts from square one.
It seem my prior employers were providing information down to gross and net pay PER pay cycle, with details about my medical, dental and vision insurance coverage [!!]
This is from Equifax, the company that got hacked and lost PII, and they are getting extremely detailed information!
Every employer should be ready to resolve "discrepancies" that come back without any negative thoughts about the potential employee. If they can't or won't do that, I don't think you want to work for them.
A few years ago, I was involved in a spinoff and they decided that all the employees would need to go through a background check. Of the ~90 people, something like 10 people (>10%!!!) had weird stuff that turned out to be completely wrong. For example, one person was reported to be currently in prison 5 states over. Some others were "we can't verify this person ever worked for ABC Corp". We were ABC Corp.
Most of these background check companies, they'd say of course there are a lot of Mike Smiths around, but Patty Jones? No no, there has only ever been one Patty Jones in all of human history.
That was after their initial email to me:
"Hi, we're about to start your background check. Just want to confirm that this is the correct email address for you?
Are these also the correct details for you? [And proceeded to list Full SSN, address, DOB]."
Like, I'm really rather glad that this actual _was_ the correct email address. But in any case I was furious. On both counts.
In credit to my employer, once I reviewed these two things with them, they fired the background check company.
I don't know how it works if you accept the NDA and get promoted within.