Actually, that is false, because what we use when we compare productivity across countries is real GDP, which is the GDP adjusted for the price level in the country. So when the price of oil goes up, the value of oil production goes up, but in fact the volume of oil production may not be changed. And it's the volume of oil production that goes into real GDP, so you won't get that kind of spurious effect from a change in the price of what you produce when you look at productivity.
Clearly, higher oil prices are inducing a lot more investment in oil and gas exploration in Alberta, and they're certainly giving people more spending power, which is boosting GDP in Alberta. But the simple fact that the price is higher doesn't have an impact on the GDP measures or comparisons.