It's hard to say with any certainty, but if your insurer was not involved in the claims process they would probably never know. If they do become involved they would likely know that a claim had gone through another company.
The best course of action would be to call that insurance company and request all paperwork associated with that claim. It should show as a zero dollar payout, which you could show to other companies to dispute the claim.
As long as your license wasn't suspended as a result — or other violations that affect your driving record — you do not have to report fix-it tickets to your insurance company. Insurers typically will only rate against moving violations that show up on your motor vehicle record (MVR).
I would call my prior insurance company (your renters provider) showing the false claim and see how they have it marked. I would also have them send confirmation that the claim was dropped and not paid out.
I would contact the insurance company that listed the claim and start a dispute. They really shouldn't be able to put you down for this claim. I imagine it was an error made on their part if it wasn't even your insured vehicle.
Claims departments should be marking the correct driver for a claim but other drivers pop up on reports from time to time. This comes from the way the insurance company generating the quote is reading reports.
Unfortunately, if you start the claims process, the insurance company can list it on your CLUE report through LexisNexis which contains your claims history — even if there was no payout or resolution. You can dispute with State Farm to see if they will remove it, but at this point, that is really the only option which is definitely frustrating.