Exactly, this misconception is being repeated everywhere. It often goes up with inflation, not because of it. An asset with shrinking circulating supply will go up in price. It's self reinforcing because hoarding reduces the circulating supply. This is deflation and it's self reinforcing nature is why it is considered bad in economics.
This happens completely independently of USD inflation. If USD inflation goes up then Bitcoin may go up by the same amount. However, inflation may affect hoarding instincts in either direction, which can wipe out the influence of inflation on the price of Bitcoin.
For example, people may liquidate Bitcoin to buy commodities that are going up in price. The gasoline pipeline incident causes a shortage of gasoline, people start hoarding gasoline because it goes up much faster than the CPI average but Bitcoin itself can only protect against the CPI because Bitcoin holders want to buy things other than gasoline. If you are a consumer that needs nothing except gasoline then you would believe your Bitcoin are worth "CPI Bitcoin price" * (1+gasoline inflation rate). E.g. 25% gasoline inflation means it is worth 25% more than market rate, because you need 25% extra just to stay where you are.
The obvious problem is that there are some goods that went down in price. Assuming 20% deflation, someone else is willing to accept 20% dollars less for his Bitcoin. The average of both is 5%, therefore the "CPI Bitcoin price" would go up 5%. However, since the gasoline guy wants the 25% gains, it makes more sense to liquidate Bitcoin and buy gasoline directly but the deflation guy remains, which paradoxically drags the price of Bitcoin below inflation because it no longer tracks CPI but rather the CPI without the things that went up.