Does this effectively rule out my plan? Can a non-US person not sell in the US because of this?
No, this won't rule out your plan. There's a lot involved in starting a company in the U.S. (the form of the company, what State you operate in, etc.). But I'll restrict this answer to the new tax filing requirements of PayPal. You can either use an SSN or an EIN number. An EIN number is much easier to get.
Here are the appropriate links:
I'm being voted down because I mentioned making a company in the United States. Obviously you don't need to set up a company to get an EIN (nor did I suggest that). However, there are legal and tax benefits to setting up a U.S. company (see a lawyer/accountant).
But this answer is right about needing an EIN, SSN (or the unmentioned equivalent of an SSN the TIN). That is, there's a new law for payment processors that are based in the United States and they require this tax ID whether you're from the U.S. or not. It just came into effect in the last several months.
In fact, PayPal says as much:
Are non-US PayPal accounts affected by this new law?
Internal Revenue Code Section 6050W requires PayPal’s non-US subsidiaries to comply with the new law. As a result, non-US account holders may need to certify their non-US status and their address. US sellers using a non-US PayPal account may be required to provide a tax ID number (Social Security Number (SSN), Employer Identification Number (EIN), or Individual Tax Identification Number (ITIN)) for those accounts. We will provide additional guidance on these requirements when available.
But, I suppose the commentors on this answer were right about the "forming a U.S. company" bit of my original answer. You don't need to form a company.
You do, however, need a U.S. tax id (SSN, EIN, or ITIN) if you're going to use a U.S. based payment processor.