There are some details missing, like what your country of residence is, but most large US-based multinationals use HR vendors that make international hiring straightforward. In my experience, that usually translates to being hired as an employee of a regional subsidiary of the parent company, operating in your country.
If it's a small company, that's probably way too expensive and they would need to set up the appropriate operating entities, etc. The contracting offer makes sense in that scenario, but it's a contract and you should negotiate comparable terms.
IMHO, it's okay to be polite and direct with the hiring manager or recruiter. You promised me <x> but offered me <y>. I understand that this might be a result of complexity hiring in <home country>, can you help me understand the detail and work with me to make this new offer equitable? My concerns are that I am no longer guaranteed <x>, <x> or <x>. What can we do?
If they're not willing to have that conversation or resolve those gaps in compensation or equity (totally agree with other folks here that US-employment is generally at-will on the part of both the employer and employee -- your rights as a worker here generally suck compared to other places, and let's not even start on the topic of healthcare and insurance), then I agree with the "this is a bait-and-switch" sentiment.
At that point, you get to choose to take the role under the offered terms (you've got money coming in, and you can keep looking for a better opportunity while performing that role), or you can pass and find a less shady employer.