Not true. The US and Canada has a tax treaty which means any Canadian taxes you pay count against US taxes owed. In other words, you only have to pay US taxes if your tax liability is lower than what it would be in the US.
Since Canadian income taxes are higher than US income taxes, you'll never have to pay US income taxes (baring some odd financial situation).
Since Canadian income taxes are higher than US income taxes, you'll never have to pay US income taxes (baring some odd financial situation).