Misleading implies the data has some agency. Data cannot be misleading. People can make whatever conclusions they want based on data at hand and it’s just bad analysis if it’s wrong. The data didn't mislead them.
Sort of. BLS also publishes other numbers. Media outlets choose which one to report.
Consider how last month everybody was reporting Core-CPI because it was higher than overall CPI and therefore produced more urgent sounding headlines whereas earlier in the year when overall CPI was higher that was the reported number. Yes, headlines said "Core-CPI" last month but if you aren't careful you get a very incomplete picture of things.