The problem with working for the U.S. company directly is that you'd be a W2 employee residing in Canada. According to someone on this forum, in your situation, who paid for legal advice - this is at best very complicated and tricky, and at worst illegal. As a W2 employee (that's the possible illegal part) you'd have U.S. taxes withdrawn on your regular pay. You should also be making quarterly tax payments to CRA. So, you'll be making double tax payments. Come tax time, you'd attempt to "claw-back" all the taxes you paid to the U.S., so that ultimately you are paying taxes to just CRA (as you are a resident of Canada).
Back to the PSB. It appears that you can be classified as a PSB whether you're self-employed or incorporated. So, why does the U.S. company want you to incorporate? Here's one guess. In the scenario below (from the link pasted further below), assume that you are Ellie and your U.S. company is Techco.
"One reason that Techco might want to set up a contract for services with a corporation instead of directly with Ellie is to make it clear to both Ellie and the tax authorities that she is a contractor to the company and not an employee of Techco. If Ellie is not an employee, Techco will not be obligated to pay employee benefits, nor will Techco be required to deduct and remit payroll source deductions to the Canada Revenue Agency (CRA), such as employee income taxes and Canada Pension Plan (CPP) and Employment Insurance (EI) premiums."
The article then goes on about the thorny path of being declared a PSB, including the possibility of paying 44.5% taxes.
Tucked away in all this doom and gloom (keep in mind that BDO is posting this in hopes of getting your business) is the following...
"If you find yourself in this situation, it is likely beneficial for the corporation to pay out the PSB income as remuneration (as earned) to you, the incorporated employee, and comply with any corresponding payroll and remittance requirements. "
So in the end the conclusion appears to be....
Incorporate to protect the U.S. company so that they're not on the hook to comply with CRA.
Assume you'll be declared a PSB, but you'll pay all of the corporations income as salary to yourself and presumably avoid the corporate PSB tax hit.
Or at least that's my understanding of all of this. It's just not clear to me why all these doom and gloom articles on PSB don't highlight the possibility of paying out all income as salary to avoid the PSB corporate tax rate. Perhaps it's because some will want their cake and eat it too? Attempting to get the lower small business tax rate (i.e., lower than personal tax rates), while really being a PSB??
https://www.bdo.ca/en-ca/insights/tax/tax-articles/psb-rules-case-study/