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.