Most companies hiring remotely don't have if your 1-person company is US-based or not.
The ones that care to hiring within vetted countries for $reasons usually will not accept exceptions. Notable example is GitHub which has a list of countries they hire from (even though they're owned by MSFT and could hire on the Moon if they wanted).
Having a company is mostly for tax purposes. It makes everything easier. I think the hiring company doesn't care if the contract is done with a business or an individual. Both are usually limited liability and offer no advantage in case of contract breaches.
But ultimately it depends on the motivation of the company itself, and they use all sorts of excuses to not work with non-US staff