HSBC had the most succinct summary I’ve seen: https://www.fatca.hsbc.com/-/media/fatca/pdfs/global---commo...
The Australian Tax Office has a reasonable guide on the overall scheme and how it applies: https://www.ato.gov.au/General/International-tax-agreements/...
The banks deal with FATCA with checkboxes. If you cross one incorrectly, I can imagine they need documentation for that. And no bank wants that.
This is purely a procedural thing for a bank. If you qualify as a US Person then the bank is going to withhold additional tax on your accounts and you’ll have to get a rebate for any discrepancies you are owed when you file your returns. While I hate the whole process and think it’s a gross overreach by the US gov, it’s governance 101 stuff for a bank. If you’re dealing with a bank that is incapable of doing this I’d recommend finding different bank. This is like the “no brown m&ms” basic competency check in a band’s tour rider. If they’re not getting this right then who knows where else they’re incompetent.
My initial assumption that seems to be confirmed by HSBC and the ATO is “no”.
But I'm not 100% sure.
However, are you sure that simply by owning a US company you become a US person? Because according to my understanding if you don't live in the US (and don't spend more than 4 months / year there) you wouldn't actually be tax resident in the US and therefore also not be a "US person".