Presuming adoption of the treaty, it deals mostly with the past. In the future, if there is no tax obligation because the withholding tax is eliminated, the payments will be taxable only in the country in which the lender carries on business and is resident. But today the situation you've described is correct. The tax charged on the interest paid and withheld by the Canadian payer in the examples we've been talking about—again, it works both ways, but we're talking about payments going from Canada to the United States—the tax withheld by the Canadian and remitted to the Canadian government legally represents a tax on the non-resident, on the American lender who's receiving the interest payments.
The American lender, in calculating U.S. tax liability, will figure out how much its net income is, multiply that by a specific tax rate that applies in the United States, and subject to a number conditions, of course, will be able to deduct the tax paid to Canada from the U.S. tax liability. The situation will work in reverse for a lender from Canada lending to the United States and receiving interest from the United States.