If $X needs to increase because they can hire/retain the people they want, then $X needs to increase.
The government publishing a single inflation numbers is kind of irrelevant to the equation. If they can keep hiring/retaining the people they want, in spite of inflation going up, then nothing has to change.
I can't imagine it being that hard to imagine :) considering this is the second paragraph of wikipedia[1]:
Prices will not all increase at the same rates. Attaching a representative value to a set of prices is an instance of the index number problem. The consumer price index is often used for this purpose; the employment cost index is used for wages in the United States. Differential movement between consumer prices and wages constitutes a change in the standard of living.
What really makes a difference is how much a competitor is willing to pay, their scale, their work environment, and how well they sell themselves.