Yes, but which taxes? As usual, the devil is in the details.

Some categories of income are taxed only in the country where the income originates (via exemption or via tax credits), or at a lower rate (via tax deductions). So, your generalization does not hold.

As a simple example, cited in the Technical Explanation (pg 74), capital gains on US real estate earned by a Swiss resident (whether a US or a CH citizen) are exempt from Swiss taxation:

"Gain from real property situated in the United States...[is] exempt from Swiss taxation if U.S. taxation on such gains is demonstrated by the Swiss resident."